1. Why does this happen? 2. How do you fix it? 3. Is it your internet connection?
1. It happens because someone is playing on a damaged disc, so their X-Box cannot read the map correctly.
2. You fix it by either taking care of your disc, or by downloading the disc to your hard-drive. (it's best to borrow someone's undamaged version of the disc to download)
3. To an extent. If your connection is too slow it will sometimes not be able to load the map on your console and you will get a failure to load. However, this rarely happens due to a connection.
This happens when your disc is so damaged that your console cannot read all of the maps properly. However, if you download an undamaged disc to your hard-drive, it will load from your hard-drive rather than the disc. This means that unless your disc becomes completely unreadable (shame on you for letting that happen, btw) your x-box will load the undamaged version of the game from your hard-drive every time, preventing a failure to load.
Mind you, it only takes one person in the lobby who is unable to load the content to cause a failure to load to happen, so spread the word.