On the page https://cloud.digitalocean.com/settings/applications I just noticed that I have a "DigitalOcean Community" app which has 'full access to [my] digital ocean account'. What does this app do? What would happen if I revoke its access?
You are in the community app when you ask your questions. That is what it is. If you revoke the access you will not be able to ask questions etc for help.
if you ask questions in the community then you are included in the Digital Ocean Community when you have a full-fledged access to your Digital Ocean Account. If you revoke the access then you are no longer a part of the community. Hence, you can neither ask questions nor answer any of them.
Answered https://www.digitalocean.com/community/questions/apps-api-digitalocean-community