The crust is coffee that hasn't sunk yet.
Grounds float at first, pushed up by gas. Breaking the crust lets them sink and finish extracting; skimming removes what would make the cup muddy.
What it is
In a French press, the layer of grounds that floats on top early in the brew, pushed up by gas.
Why it matters
Grounds left on top extract less. Breaking the crust sinks them so they finish extracting; skimming the foam removes bits that would make the cup muddy.
In practice
After about four minutes, stir the surface gently with a spoon, then spoon off the foam and anything still floating.