Proxies are when you create Low Resolution images of the hi end stuff you shot (like 2K or 4K images), and edit with the low res images on your small computer. Then, when you are ready to finish, or conform, you match back to your original files, capture just the files that you actually need (because they are so large), and finish your show, with just the 2K or 4K files.
This process has been happening since the stone age, when 1" and 2" analog VTR's existed, and people would do "off lines" with 3/4" Sony VTR's. Of course, there were no proxy files in those days, because
NLE editing was not invented yet.
Another major use of DI is for the die hard film people who like to shoot their movie's on celluloid.
They take their 16mm, 35mm or 70mm film from their Panavisions etc, get it processed and run it thru a Northlight Film single frame intermittent scanner etc at 1 frame per second at 4K into a massive storage array which also creates proxies.
Then all the editing is done NLE using the proxies, and CGI, titles etc are added, tradition cinema audio post is done, and then the whole lot is colour graded and ends up getting digitally lasered back to film for release.
All rather amazing really.
On line Mastering Facility
FCP, Avid, Adobe