NOTE: checkouts and repositories do not exist yet
In the simplist of terms, a branch is the information stored along with a [:WorkingTree:working tree] that gives you access to revision control. One of the most important pieces of a branch is the record of all of the previous [:Revision:revisions] that the working tree has ever had.
Sometimes a branch, named a [:StandaloneBranch:standalone branch] will directly store its own [:Revision:revisions]. At other times, such as when a branch is a [:Checkout:checkout] or is a part of a [:Repository:repository], the revisions elsewhere.