A vassal state is like when you have a bigger friend who helps you and protects you from other people. But in return, you have to be their friend and do what they say.
In the old days, some countries were vassal states. The big and powerful country was called the suzerain and the smaller country was the vassal. The suzerain would help the vassal in battles and keep them safe from bad guys. But the vassal had to be loyal to the suzerain and give them tribute, which was like a present of money or valuable things. The vassal also had to do what the suzerain said and follow their rules. It was like having a boss or a teacher who says what you should do.
So, it's like when a big brother or sister helps and protects their younger sibling, but in return, they have to listen to what the big brother or sister says.