The Overrun command card states " Use at the start of your activation. During this activation, when you enter a hostile figure's space, that figure suffers 2dmg . Limit once per hostile figure."

I assume that means it can hit multiple hostile figures... and it also triggers on moving past them and not just ending the move on top of them?

Am I correct in that understanding?

You are correct, As long as you enter the space the damage is caused. You do not need to end your movement on their space.

A figure also enter s all spaces it moves through whether the space is shared with another figure or not.

Overrun...as in "to run over", as in "IT'S A HIT N RUN HOLIDAY!!!! WHOOOOOOO!!!"