First off, if you're playing on mobile (Android/iOS), unfortunately you don't have Ginger Island + many other features that the 1.5 content update added.
But if you're playing on any of the other platforms (PC, Switch, Xbox, PS), then you'll have it, which is great!
––––
Once you've completed the Community Center, you'll get a letter from someone, inviting you over. Go to their place of residence. A cutscene will play, and after that you'll be tasked with gathering some resources.
If you've collected everything, a new area (Ginger Island) will be accessible.
Ginger Island is an island full of puzzles, mysteries, and upgrades. You complete tasks and unlock cool stuff!
There will be new quests and things to do, but none of them are "essential" to Stardew gameplay, they're all bonuses.
Pretty much, Ginger Island is the host of a whole suite of endgame activities, all of which I found fun!
Hope this helps!