Among the Picard Options there are choices to rename and move files to new locations if you want to. Look under “File Naming”. This will start building a file structure with the newly identified files. It also lets you set the file name pattern.
Be aware of the different coloured icons appearing on the right hand side. This tells you how good a match Picard thinks it has for the track. Are these tracks parts of full albums? Or just loose and random files? You will have more chance to get accurate matches with the former.
But “am I missing something” - it depends what you think Picard is. It is a tagging tool for tagging music files that you the human have already organised. It does expect some level of human checking. Picard will look up an album in the MusicBrainz database and then return with a “best match”. This isn’t always perfect so will need to be checked.
I have noticed a lot of people pick up Picard as they think it is a tool that will magically identify a heap of 1000 badly named and badly organised MP3 files. Thanks to the AcousticID technology built inside this is something it can kinda do pretty well… but it also is not perfect and will get many matches wrong. All depends on the quality of the start data.
Expect some tracks to be easily matched up… but others will need you to check them manually. Especially if they are just random loose tracks which are not part of an album.