I used git worktree add to create a new worktree. I noticed that is has created a new branch in the repo with the same name as the worktree. What is this branch for?
I have checked out an other, pre-existing branch in the second worktree. Am I free to delete the branch that git worktree add created?
The branch is necessary because you cannot have the same branch checked out in different worktrees at the same time.
So if you do not specify a branch when adding the worktree, then git will add one automatically, based on your current branch and with the name of the worktree directory.
You may ask, why cannot I have the same branch checkout out twice? Think of what will happen to worktree A when you commit to B, if they both share the branch... the worktree A will see the commit in B as a local difference, but in reverse! just as if you did git reset --soft HEAD^... That would be quite dangerous.
BTW, that is the same reason why you cannot push to a branch of a non-bare repository that is checked out.
About your last question: can you delete the branch? Of course, that branch is in no way special. You can delete it as long as it is not checked out anywhere.