I'm a psychotherapist by training so go easy on me here. I would like to know, in simple terms if possible, the basic mechanics of how Hubble can see back in time.
I pretty much understand, in this case, that light has to travel extremely long distances to be captured by a lens. I think the key point I'm missing is how long did, for instance, the light from the deep field shot, take to reach Hubble's lens? Really appreciate any help. And please keep the answer on beginner level please?
You seem to already know the answer. You "see back in time" exactly the same way you can "hear back in time" during a thunderstorm...
You know how they tell you to start counting seconds when you see the lightning, stop counting when you hear the thunder, then divide your count by five, and that's how many miles away the storm is?
So the lightning arrives almost instantaneoulsy, while the thunder travels much more slowly. So when you finally hear that thunder, you're hearing what happened in the past. Indeed, five seconds in the past for every mile away the storm is. And that's simply because it takes thunder (i.e., sound) five seconds to travel one mile.
Exactly the same thing for light. One year in the past for every six trillion miles away the star (or whatever you're looking at) is. And that's simply because it takes light one year to travel six trillion miles. (And, by the way, they colorfully name six trillion miles "one light-year").
Other answers have detailed exactly what the mechanism is, or have given analogies that demonstrate similar principles, but I wanted to find a better visual representation of what's going on. Unfortunately I wasn't able to find exactly what I'm envisioning, but I got pretty close:
So what are we looking at here? Well, picture the Hubble (or technically any telescope) being on the left, taking a peek at a section of the sky. The whole image that you see through it would be all three of these "planes" combined, it would look like one flat picture. But we know intuitively that not all of them are the same distance from us, so hook that into knowing that light takes time to travel any distance, just like everything else, and you might make the connection that you're looking for.
The light from the closer objects that you're seeing (the left plane in the image) is "newer", in that it took less time to reach you. The light from the farthest objects (the right plane) is "older", having taken a longer time to travel the distance from the source to you. So with that in mind, take another look at the diagram and try to visualize a snapshot of space the same way. Any random view of space works. The light is all arriving at your eye at the same time, but some of it was emitted recently, while some was emitted way further in the past and took a longer time to reach you. Thus you are never seeing things as they are "now" but how they were X number of years ago (X correlating with their distance from you). This is where the term "light-year" comes from. If an object is 1 light-year away, it took the light from it 1 year to reach you. In the diagram that translates to the objects in the left frame being about 0 to 5 billion light-years away, the right frame showing objects that are more than 9 billion light-years away, and the middle being somewhere in between.
That's why telescopes can "see back in time". That phrase is somewhat misleading, because it sort-of implies that they can see things in the present too, which they technically can't. But what it really means is that the farther you can see, the further back in time you are looking. That's part of the reason we're obsessed with building longer-range telescopes, to get a better idea of what the universe looked like further in the past.
Edit: I just remembered an episode of Cosmos (the new version) that deals with this topic, though it delves into the space-time side of things a little deeper. It has a decent explanation of why a telescope can "see back in time" and then goes into explaining the relationship between light and time, and the history of how we discovered it. If you have Netflix you can watch it now, or you might be able to find it through other services. The episode is called "A Sky Full of Ghosts".
Short answer
Simple. It sees back in time in the same way that literally all of us see back in time, all the time.
Long answer
One of the most important observations in all of physics is the finiteness of the speed of light. (One of the first substantial pieces of evidence for this fact was actually demonstrated in 1676 by a Danish astronomer named Ole Rømer, well before Einstein incorporated the finiteness of the speed of light into his theory of relativity). However, the so called "speed of light" actually has very little to do with light; instead, the speed of light determines the maximum speed at which any fundamental interaction of nature -- and therefore transfer of information between two bodies -- can take place. In his Course Of Theoretical Physics Volume 2: The Classical Theory Of Fields, Landau appropriately introduces the speed of light as the maximum velocity of propagation of interaction, and an excerpt from the first chapter of the book in which he talks about the implications of this maximum velocity can be found in this answer.
The main implication important in the situation you bring up is that since light propagates at a finite speed, the light you see coming from any object you look at was emitted in the past, firmly located on what's known as your past light cone. For example, since the sun is approximately 500 light-seconds away from Earth, whenever you look at the sun, you are seeing the sun as it was 500 seconds ago when it emitted the light, and you will not see what the sun looks like now until 500 seconds have passed and the light emitted now has reached you.
Of course, this is not the only consequence of the finite speed of light. All of the unusual affects associated with relativity result from it as well, and I'd highly recommend that you read more about this very interesting subject.
The Hubble has spotted a galaxy that is 13.4 billion light years away. While we see the moon as it was 1.5 seconds ago, or we watch Mars rovers' "7 minutes of terror" live, as it happened 10 minutes ago [I always wonder if prayer works outside the light cone?]--the significance of the Hubble seeing back in time is that the Universe is only 13.8 billion years old--so it's looking back over 97% of all time that has ever existed in the Universe--and that is amazing.
If object emitting a photon (= one ray of light) is so far that it takes a year to reach the observer then what you see now by looking towards the object is actually what it looked like a year ago.
A telescope looking at space will see multiple stars that are each in different distances from the telescope. So the photons from them, while being equally fast, have traveled for different durations.
Light travels with a speed of $300\;000 \mathrm{km/s}$ through space. If you google any space object, it should be possible to find its distance to Earth. Wikipedia is always quick and helpful.
And then you can calculate the time it has taken the light to reach Earth:
$$time=\frac {distance} {speed} $$
As an example, it takes light from the Sun approx. 8 min to reach Earth. When you look up and see sunlight, you actually see 8 min old sunlight. What the Sun looks like when you look at it is in fact how it looked 8 min ago.
You know when you hear your own voice's echo? That's hearing yourself, say, 2 seconds ago.
1 second of that is for your emitted sound to hit a wall, and 1 second is for it to travel back.
That means the wall is also hearing you back in time 1 second.
Telescopes are just like the wall here; like the wall hearing the past, they see the past.
The only difference is that instead of a 1-second delay it's often more like 1 billion years for stars.
Strictly for the non-scientists:
Light moves amazingly fast by human standards - about 300,000,000 meters per second, which for Americans translates to over 670,000,000 miles per hour. Most things we see in everyday life are seen "now" for practical purposes. If you could guide a beam of light around Earth using prisms and lenses, it would go full circle in about 1/7th of a second.
But when it comes to astronomical objects such as the Moon, the Sun and the planets, the distances are astonishingly large. For the Moon at about 1/4 million miles away, light (or radio) takes around one and a half seconds to span the distance. The Sun takes eight minutes - we say it's eight light minutes away. Using time to describe distance is like when someone talks about someplace to drive to - "it's twenty minutes away."
I worked with the Cassini spacecraft - it was over one hour between when the spacecraft started sending image data, and when we'd start receiving it. Saturn is over one light hour away. It's like slow postal delivery - you get news of what happened, not what is happening. What happens at Saturn remains unknown to us on Earth until light (or radio, or x-rays, or whatever) has had the time to travel the distance. So when we look at Saturn right now through a telescope (or with bare eyes) we see how it was as of one hour ago.
Stars are much much farther away then anything in our Solar System. Light takes years to span the distances between even the nearest stars. Alpha Centuary is about four light years away from us. If it were to suddenly flare up, we wouldn't know until four years later. What we see today looking at Alpha Centuari is how it was four years ago. We can't know any better, since nothing (we know of) travels from the star to us any faster than light.
Most galaxies was can see in typical affordable telescopes are a few million light years away.
Hubble's Deep Field image was taken when aimed at a part of the sky with no stars of our own galaxy in the way, and none of the "nearby" galaxies only millions of light years away. The galaxies visible are several billions of light years away. So, we only know how they looked as of several billion years ago. Reporters who like to say intriguing things then say "Hubble sees back in time" as if it were some magical metaphysical device. No, it's just "slow" messengers of light.
