*Update 11/15/2009* There are now several apps that let you create and edit groups on the iPhone. Some examples are Groups (iTunes link), YoContacts (iTunes link), and iGroupMail (iTunes link)
To create a group of contacts for your iPhone, you must use the program Address Book that ships with every Mac. To create a group, open the progam, Click File, and select New Group:

A group is made up of multiple contacts, and only those contacts appear on screen when you select the group. For example, you could label all your family contacts under a group called “Family.” A group like this could come in handy if you wanted to make calls to all your family members in an emergency or to make an announcement.

Groups created in the Mac program Address Book
For now, groups cannot be created using just the iPhone, nor can you remove a contact from a group. The only thing you can do with groups using the iPhone is create a new contact inside a group. For instance, if you navigate to the group “Work,” and create a new contact by tapping the “+” icon, that contact will be added to “Work.” Hopefully, the option to create and edit groups using the iPhone will appear in the future.
Helpful Link:
Discussion of groups at Apple.com.

#1 by Rudytaylor3rd@mac.co on October 6th, 2008
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After the group has been synced to Iphone I cannot remove it from phone even if I delete in address book? If so how.
#2 by Alan on January 17th, 2009
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Delete the group from the address book, synch the iPhone, and it will disappear from the iPhone.
#3 by Dax on November 15th, 2009
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Can you send a text to a group all at once? I want to type one message and send it to the whole group, is that possible?