Maximum resolution (1280×720) is the full HD cover image. Use it for blog posts, video research, presentations or thumbnail design references. Not every video has one — it depends on what the creator uploaded.
SD (640×480) and HQ (480×360) exist for essentially every video ever published, which makes them reliable fallbacks for older uploads.
MQ (320×180) is the small preview size, handy for listings and link cards where a large image would be wasted.
A note on usage: thumbnails are the creator's copyrighted work. Downloading one for research, commentary, criticism or as a design reference is generally fine, but republishing it as your own is not. If you're studying what makes thumbnails perform, collect them for reference and then design something original.