Facebook recently changed the way Groups work. Before when someone saw a group they thought some of their friends would like, they could select the names and “suggest” it to them. Now, if people do this with an Open group (one that does not need an administrator to approve membership); then you are automatically added to that group and the joining activity is shown on your wall.
If you want to leave this group, simply click Leave Group. After you do this, nobody else will be able to automatically add you to this group, but you can rejoin later if you want to to so. More details on this here.
Posted in: Facebook