Actually it means nothing and is ignored.
This often happens when output from multiple places is combined and it isn't clear who's job it is to add the slashes, so both parties do it and you end up with two of them. Semantically in the case of a directory path is has no meaning and will be ignored by most programs.
There are other situations in the unix world where they have meaning. Sometimes at the start of a path they could trigger a search for a samba path instead of a local file system path, or after a protocol in nfs they can indicate a hostname, however particularly in the case of a trailing slash like you gave as an example, it shouldn't matter much.
For the sake of your sanity as an administrator or programmer you should still avoid these cases wherever possible. You never know when something will be parsed incorrectly, but if one comes your way don't worry about it.