A critical strike deals extra damage during an attack. This could represent an attack that hits harder, a lucky strike or damaging a weak area on an opponent.
Crit chance stacks linearly. So a 20% chance + 10% chance nets you a 30% crit chance. You can break 100% and crit on every single hit. Same with Crit Damage. Critical damage is a proc'ed effect so it's proc'ed by your AA. Burning Blade, Pyre, and other On-Hit abilities are proc'ed by the AA; it doesn't count as a source of on-attack proc's in and of itself anymore than Pyre, Sliptide, or the others.