,and also the hardrive and thumb drives on xbox 360
The memory card is more commonly known as the hard-drive. the hard drive is used to store information such as saved games, music, and downloaded games and content. As majikthise said, you can take it to your mates house and play games you have saved on that hard-drive on your mate's xbox counsel.
You can use it to store game files, and then take those files to use on another Xbox, e.g. at a friend's house.
You may find it helpful to read the following.
Oh, and welcome to the site.
-- Best wishes - Majikthise.