In general, spin affects the direction in which the ball will travel after hitting the ground.
Back spin and top spin requires you to unlock clubs with the ability to use spin.

With the right set of clubs, you'll be able to add back spin to your shot by tapping on the golf ball icon on the right when you're taking your shot.
This will bring up the ball spin mechanics where you can rotate the ball downward to add back spin.

Shots with back spin will propell the ball backward after hitting the ground, which can help make the ball travel less after landing or travel backwards.