In my humble case, Docker solves the problems I have to manage the systems on which my application runs (and that's mainly it). A single dockerfile of 20-30 lines describes a whole system (operating system, versions, packages, libraries, etc), and cherry on the cake, I can version it in my git repository.

This is not revolutionary in itself, but having the creation and deployment of a server being 100% replicable (+ fast and easy!) on dev, preproduction, and production environments, plus it's managed with my usual versionning tool, that is something I appreciate very much.

Sure, there are other tools to do the same, but docker does the job just fine.