A pushover is a person who's easy to fool or influence. A substitute teacher who's a pushover is easily convinced that the class usually spends an hour watching music videos.
If you're a pushover, you find it hard to deny anyone what they ask for. If your mom's a pushover, it means it's a breeze to get her to say yes when you ask for something. A babysitter who's a pushover will let the kids stay up way past their bedtime. If you think about it, the word makes sense: if you can push someone over easily, then that person can't stand up against you. Around 1900, pushover meant "an easy job or task," and by 1922 it also referred to people.