git branch -D <branchName> will delete your branch from repository. You will not be able to see it or navigate anymore. Also you will lose all file changes made in that branch.
Git branches are stored as references to a revision. If you delete the branch, the reference is removed; if nothing else references that revision, it will eventually be garbage collected. Also, if you delete the branch then it's properly gone (from your repository). If you want to mark a branch as deprecated but keep it around for later use, you could move the branch to a subdirectory:
Alternatively, you could create a separate repository for deprecated branches, pull them across then delete them from the original. In either case, you're going to affect any users who are following the branches -- the content of their repository won't change (and neither will any of their branch names), but if they try to pull again, they'll have to change their target in their configuration.
You can delete the branch, but tag it first, so that it's history doesn't disappear. This way, the branch doesn't show up in the branch list, which should hopefully deter people from working on it, but the work won't be permanently erased (even after garbage collection is run). For instance, whenever I have a branch that has become irrelevant, but I'm not prepared to permanently delete it, I tag it as "archive/<branch-name>".
While on master or some other branch:
git tag archive/foo foo
git branch -D foo
This creates a tag named archive/foo from the foo branch before deleting foo. You can also add a message to the tag, that explains what is in the branch, why it existed, why it's now a dead end, etc.
git tag -m 'Foo is deprecated in favor of bar' archive/foo foo
The ability to record why a branch is being deprecated is perhaps an advantage of tagging versus moving branches to an alternate namespace.
If you ever need to resurrect a branch that has been archived this way, it's as simple as:
git branch foo archive/foo
git tag -d archive/foo # Optional
Now the branch is back as though it was never deleted.