In Bitbucket, the base branch is the last branch that you have selected from the list of branches. If you select another branch in the drop-down menu, you will see how the “base branch” icon moves to the newly selected one.
In Git itself, there is no base branch concept. This was answered in What is the base branch when a new one is created?
The default branch is master (you will be on this branch after a clone or when browsing a repository). In Bitbucket you can change the default branch in the Repository Settings screen.