Off the top of my head...

1. Removing spam
2. Reviewing flagged posts and actioning them as needed
3. Ensuring that posts follow the community rules
4. Organizing events and contests for your userbase, if applicable

It can definitely be a thankless job at times, but also very rewarding to see the community flourish.

Not specific to Lemmy, but basically you remove spam, offensive posts/comments and cultivate the space the way you think it should be.