Hello there!
Let me explain a finite potential barrier like you're five years old. Imagine you are playing with your favorite toy, but it cannot go through a gate because the gate is too high. Your toy is like a something called a "wave" which is like a little bump that travels from one place to another.
A finite potential barrier is like that gate, except that the wave can sometimes go through it. In science terms, a finite potential barrier describes a physical barrier that has a certain height or strength, which can be passed through by a wave if it has enough energy.
This is similar to when you jump over a very high jump rope. If you don't have enough energy or strength, you won't be able to jump over it. But if you have enough strength and energy, you can jump over it!
So, in a finite potential barrier, if a wave has enough energy, it can go through the barrier and continue on its path. But if the wave doesn't have enough energy, it won't be able to get through and will be reflected back.
I hope that helps you understand what a finite potential barrier is!