A backend is a part of a program which receives commands from the frontend (the user-facing part of the program) and performs some actions based on the input received before sending the result back to the frontend.

A GPU (graphics processing unit) is a piece of hardware which is very good at doing a lot of calculations with a lot of numbers very quickly.

Making a backend for the GPU means programming the backend in such a way that it can run on the GPU, thereby (hopefully) getting the program to run faster and more efficiently.