Managing an e-mail inbox or two can be a full-time job in and of itself. If you find yourself having to continually apologize to people who ask, "Did you get my e-mail?" because you have lost control of your ever-expanding inbox, perhaps iOS 6's VIP inbox feature can help.
Open the Mail app and from the general Mailboxes view, you'll see a VIP line wedged between All Inboxes and your mail account(s). Tap on the VIP line and you'll see two buttons: Add VIP and VIP Alerts.
Tap Add VIP and you'll be taken to your contacts. Contacts for whom you have an e-mail address are listed in black; those without an e-mail are grayed out. Tap on a black name and the person gets added to the VIP list. Tap Add VIP to add more, or swipe on a contact to delete him or her. You can also add a contact to the VIP list from within an e-mail. Just tap on the sender's name at the top of the e-mail and you'll see an "Add to VIP" has been added below the Create New Contact and Add to Existing Contact buttons.
Tap VIP alerts to change the alert style when a VIP e-mail arrives. Alerts instead of banners or vice versa, for example, or a different new mail sound. You could also turn off badge app icons for your mailboxes, and turn them on only for VIPs (I do this to reduce the urge to check e-mail on my phone, which my wife tells me I do too much).
Once you have added a contact to the VIP list, the next time you tap VIP from the Mailboxes view, you'll see any e-mails from your VIPs. To get back to the edit screen after your VIP has been created, you'll need to tap on the small blue arrow button on the right edge of the VIP line in the Mailboxes view.
If the VIP inbox only complicates matters for you, I'm afraid there is no way to get rid of it. You can, however, empty it and move it down below your other mailboxes. From the Mailboxes view, tap Edit and drag it down.