I don't know that you can create groups on the iPhone itself, but it's not the same as making a new contact. Groups are separately maintained.
Please Get the iPhone User Manual for iOS 5 might be helpful.
Here is a link to our MailShot Pro app, which leftyapple2 was kind enough to mention (Thanks). MailShot Pro in App Store
MailShot creates a special contact for your group that enables most of the apps on your device to send group email, including the Mail app itself. Just add the contact to the "To" or "Bcc" line of your email using the blue + button
Any questions or problems, please get in touch with our support email on "support at solubleapps.com", we are always happy to help.
Disclosure: we are the developers of MailShot Pro and may benefit from its sale.
What you are describing is trying to send an email to a group, which the iPhone and iPad can't do natively.
if you create a contact in MailShot, you will find it available in the list of contacts, (not on the Groups page) it looks like a regular contact to apps like Mail
Drop us a line at "support at solubleapps.com" if you need more help.
Hope this helps