iPhone 4 Contacts Group Name

The set of contacts that you see if you select "All from my Mac" are those contacts you've chosen to sync with your Mac using iTunes.
If you also had Exchange contacts, they would be listed separately, as would Google contacts etc. etc.
As long as you ticked "All Contacts" in the sync options in iTunes, the phone will have all your contacts in it from your Mac
Once inside the Contacts application, you can further choose to display individual Groups of contacts, assuming you've set these up beforehand in Address Book.

On my iPhone4, if i enter a phone number in the Phone Keypad and select the Add Contact (+ contacts icon in lower left) it opens up a new contacts page and i enter the info and save it. However the new contact IS NOT ADDED TO MY CONTACTS APP. The name of the contacts group on my iPhone is "All From My Mac" and there is no other. I cannot find contacts that i add from the phone keypad. If i enter the number in the keypad again, the contact name that i gave it magically appears under the number. But when i go back to Contacts it is nowhere to be found. If i call the number, it appears in the Recents list with the contact name and if i select the blue arrow i can view the full contact page i created. But back in Contacts i cannot find it anywhere. There is nothing in Settings that i can find to enable an iPhone contact group, nor in iTunes. Has anyone else noticed this? What's the deal?

If you already have Groups set up on your Mac, they will all sync to your phone.
All the Groups will be contained in the set called "From my Mac" and can be individually displayed by pressing the Groups button in the top left corner of your Contacts app.

To create a new contact in a specific group, you need to be in that group to start with. This is the way it works if you're adding a contact whilst using the Contacts app and you press the + button.

I just added a new contact from my "Recents" list in the phone and they appear when I select "All from my Mac".
That "virtual" Group will contain all your real Groups such as Friends, Family etc and also any ungrouped contacts so what you're doing should work.
The contact you just added is an un-grouped contact however, so if you display a specific Group, you will not see it.

As an experiment, download ContactsTap from the App Store and see if you can find the contact. If so, you can also se what Group it is in and change that Group if necessary.

If all that fails, I'd say it's then worthwhile going through the usual troubleshooting option for the phone:

Switch off and on
Reset
Restore from backup
Restore as new phone

Instruction on all of these options can be found in the User Manual.
If you done all or any of these, let us know and we'll see what else we can think of.