A bit hard to clarify in writing (easier to show) but I'll try this explanation:
Hook = a semi-circular punch powered by pivoting/twisting while your arm is held bent and horizontal to the floor, which propels your fist from left to right (or right to left). Fist impacts opponent on the side (eg ribs or side of face/chin). I assume it gets its name b/c your arm is held bent, like a hook while throwing this punch.
Cross = straight (power) punch using the rear hand, goes straight out and back. Fist impacts the opponent straight on. I think it is called cross b/c it can be thrown over an opponents jab (assuming same stance fighters) so the punch "crosses" over.
A cross can also be used to beat an opponents hook b/c its thrown in a straight line (straight line is the fastest route from point a to b.)
Hope that helps - hopefully someone can post some links to a video explanation which might be better...