In simple words: The model does the mathematics; the processor determines how it is carried out.
The processors
A Central Processing Unit (CPU) handles many general computer tasks. A Graphics Processing Unit (GPU) can perform many similar calculations in parallel, which helps train neural networks. A Tensor Processing Unit (TPU) is a specialised processor designed for tensor calculations.
When each matters
Small models can run on a CPU. Large image and language models often train faster on GPUs or TPUs. Memory, software support, data size, and cost also matter. A computer can have integrated graphics without a powerful GPU for model training.
See the flow
Editing video or training an image model may run faster with a suitable GPU, but slow storage or too little memory can still cause lag.
Remember: The model does the mathematics; the processor determines how it is carried out.