What we regard as TIME is just a way of measuring duration for various phenomena. Like a ruler is a measuring device for measuring length ( or breadth or width). Saying Time is an illusion is like saying the measuring 'ability' of a ruler is an illusion. Is a measure of length, width, or breadth just an illusion? Why do some scientists or philosophers say Time is an illusion?
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Philosophically, both time and distance are illusions. Distance is actually more disturbing than time. So first, let's define what "time" is. It is the number of transitions of an atomic state (see atomic clock wiki). Distance, a meter, is defined to be the length a photon (light) travels in $\frac{1}{299,792,458}$ of a second (source) which simultaneously defines both distance and the speed of light!
I think time is confusing because it's not well understood (for sure by the masses and perhaps even by physicists philosophically). The problem is is that if every process happened without time, then every process would happen instantaneously and there would be no existence! As it stands, processes happen as one would expect. First one thing happens, then the next, then the next, then the next, ad nauseam. This progression or chain of events, is what time actually is. If there were no "time" (so to speak) then the chain of events would happen instantaneously and no one could observe anything in the intermediate. But even that language is problematic. Because maybe it does happen instantaneously, but still the progression itself we interpret as "time".
The bottom line is that time is the number of transitions that the universe undergoes from one state to the next. This is an insanely complicated ballet that organisms with our understanding have come to interpret as time. Time is real--it is the transition from one state to another--but the perception of time as is true of all perceptions is an illusion.
p.s. And it should be noted that the term "instantaneous" pertains to time...so I am trying to describe time with our preconceived notion of what time is--which is inherently flawed (i.e. you cannot define something by using its own definition).
Jared
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You provided already the most important answer, saying
“Time is just …”
You are right: time is very much over-estimated. Time is just and nothing more than aging of matter (proper time of matter), every mass having its private time which may be observed by anybody else. You will hear many other things about time, but without any proof, without physical foundation, mere speculation, but: time is physics, time is not philosophy!
Besides, there is time measuring: Measuring means compare the time of a process with your own clock (your own aging), with the clock of something else (e.g. oscillations of an atom) or with the proper time (the aging) of the observed object.
Moonraker
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