The Target Check Card is a debit card (non-visa or -mc) that is linked directly with your checking account. When you apply, you have to give them a voided check. You can't use it at any ATM but you could get cash directly debited from your checking acct in advance of $40 including your purchase.
Why get this card? I guess if someone didn't have any credit at all and didn't have a Visa or MC check card AND they shop at Target, then it might be ideal. You also get the same awards as if you had the store card. Other companies are doing this like Wal-Mart, Exxon (w/ the speedpass), etc.