The uses are myriad, you can build Star Wars Movies, you can build computer games. You can do CAD and 3D modelling and printing, you can visualize fluid simulations
But each is an entire field.
The same with Deep Learning -
You can do image classification for medical diagnosis. Self Driving Cars. Realtime Translation. OCR. You can model chemical reactions by doing latent space exploration. You can model gene-gene interactions. You can build a image recogniser to tell if your cat is on the couch. You can build an AI that plays GO, or any other system or game where the rewards are time-delayed and sparse. You can make it play Atari games.
You can stitch satellite images together. You can reconstruct parts of photos that are missing. You can colour black and white images. You can de-noise wind sounds from microphones. You can search for comets. You can monitor deforestation. You can count cars in car parks. You can search vast ocean areas for survivors. You can build security drones that fly around at night and look for anomalies. You can turn a webpage of unstructured text into structured query-able forms (see named entity recognition). You can create visual art (google: neural style transfer)
These are just a small drop of some of the cool things that are going on - and while it might be difficult for you to advance state of the art without a GPU cluster (just as it would be difficult to advance state of the art in Graphics programming) the hobbiest can certainly start in any of these fields, just pick one that inspires you.]
EDIT: I run a Deep Learning startup - if you want some pointers or help getting started, or would like advice don't hesitate to email me - it's in my profile :)