For this picture Anna wrote: "Incandescent light is incoherent because it comes from many sources and the same is true for sunlight. By passing the light through the one slit he created a single coherent wave front."
What represent the drawn lines in the sketch about double slits? Are this wavefronts? What is a wavefront?
A wavefront is the crest of the wave. When you go down to the beach, and see those things called waves, the front is the whole line that is at the same height.
In electromagnetics, it's the same thing. It's the points that are at the same height. In your diagram, the black curves represent a unit of cycle, and the two waves through b and c can either add to each other (to get double height), or can be out of phase (so b=-c and it's nothing).
Basically, S1 produces a single source, and there is only one set of ups and downs. S2 uses two points of S1's radiation to make two points that are using the same cycles. They don't have to be in the same phase, just that their period is the same. So b and c produce waves, and these intersect, and add together based on how they are in phase.
You can see a result by draging a sine wave over another one. The crest of the sine waves are the black arcs, the intensity is found by adding, eg one wave shifted by 0.5 cycle to the other. They cancel out.
A slightly more general construction than Wendy or Bill's is
"A wavefront is a contiguous region of constant phase".
Wendy's choice of "crest" is just the selection of a particular phase ($0 \pm 2\pi n$ for wave represented with $\cos$ for instance), and that is the usual choice when visualizing wavefronts, but there is nothing that prevents you from using the trough or the rising zero-crossing or any other value.
What represents the lines are coherent photons. The only thing oscillating are photons, not waves. The photons are coherent because their all emitted in phase from the same point source. Because they are in phase gives them the appearance of a wave like this sketch:
