You don’t put anything there yourself, it’s where Hugo puts generated resources. For example, if you use image processing that’s where the processed images go. Also, playing with the awesome Hugo Pipes puts a few more files in there.
(This is my understanding as a user myself, can’t really help if you need more technical explanation.)
It is, in short, a resource cache. I put it in the project (by default, there is a setting) to make it visible – you can commit parts or the whole directory to Git, if that fits your style.
If you are theme author, you will most likely want to put the generated/fingerprinted resources as part of the theme distribution, so the users does not need to have PostCSS etc. installed to run your theme.
If you use lots of thumbnails, you may consider comitting this to GitHub to avoid having to create thumbnails on every CI build etc.
In many cases you will not need to keep generated files. If you’re using git you can prevent the generated files from accidental checkin by adding resources on its own line in your .gitignore file. If you use Atom the addition will also prevent generated files from becoming searchable within the editor.