When is the branch name updated?

I’m reading John Wiegley’s Git from the bottom up. In Introduction
he mentioned:

If you checkout a branch, HEAD symbolically refers to that branch,
indicating that the branch name should be updated after the next commit operation.

I’m confused here: for example master is a (special) branch name, it’s always master isn’t it? When will it be changed after a commit?

>Solution :

By the context, it means that the commit referenced by the branch will be changed from the current to the next created commit. The current commit is the parent (or one of the parents) of the newly created one. It’s not the branch name itself that will be changed.