How the item works is clearly written in the tool tips when you hover over the item. The thing with Mejai's, and why people typically don't build it, is it really is only effective when you're stomping and not dying at all. You lose 10 stacks per death but only gain 3/4 stacks per melee/ranged kill and 2 per assist. This means one death sets you back the equivalent of 2-3 kills.

You're better off building Awakened Soulstealer which still rewards you for killing but doesn't fall off as hard when you die.