甚至 introduces something surprising or extreme that builds on the previous statement. Pattern: A, 甚至 B - where B goes further than A. Example: 他很累,甚至站不起来 (he's so tired he can't even stand up).
usage
甚至 is more emphatic than 连...都 (even). They can be combined for maximum emphasis: 他甚至连名字都不记得了 (he can't even remember his name).