Currently it is not possible to rearrange the groups manually in your contact list; not using drag and drop nor any other method - the groups are sorted alphabetically.

However, if you happen to have a group which you consider of high priority, but its name starts with a letter far behind in the alphabet, you will this group at the bottom of your contact list - undesirably. 
Analogically, you could be dealing with a group of low importance to you that is stuck in the topmost position of your contact list. You don't need this group to be the first thing you look at every time you open the contact list.