A balance transfer credit card is a credit card that permits you to shift balance from another card onto it. Picture two mules standing next to one another. One is carrying nothing, the other is carrying 18 suitcases and a very hefty fellow named Oliver. The one carrying the weight is about to suffer a spinal collapse, so good ol' Ollie hops on the second mule to keep the first mule happy and healthy. That's basically a perfect example of balance transfer credit cards, assuming the mule now carrying Oliver has a lower interest rate than the first one, but I'll get into that later.
There are very few cards specifically designated as only balance transfer credit cards anymore. Most cards are thrown together with balance transfer capabilities, a low introductory APR, a rewards program, and a trendy sponsor to make the card look prettier, among other possible features. There are a few cards that emphasize balance transfers, though. They are cards that have lower APR and interest rates than other cards (hence the lure of balance transfers, same balance, less interest, less money being removed from your pocket), and no transfer fee.
Speaking of, beware the transfer fee. It's an easy trap to fall in to. Back up to our good friend Oliver, who was once a very successful used mule salesman. He thought it would be wise to move all of his outstanding balances onto one card that he had just gotten, as it still had its introductory 0% APR and no interest. He moved a total of $160,000. Sadly, like everyone that isn't a lawyer or accountant, he did not read the 374 pages of fine print the bank gave him, and did not see that there was a 4% balance transfer fee. He was charged $6,400, which left him just short of the amount he needed to inoculate his herd from the vicious Mad Mule Pandemic of 1999. Learn from Oliver's mistake and do not engage in balance transferring without checking the fees.
Another important thing to watch out for is the expiration of introductory rates. If your credit card has a 0% intro balance transfer rate, interest, and APR, they probably will go up quite a bit when that trial period ends, because, as far as I know, it's not profitable to not charge people for things, and most credit card issuers are pretty profitable. Know all of the expiration dates, or else you may face an ugly looking statement in the near future.
Odds are, if you own a credit card, you could probably do a balance transfer right now. If not, I'd bet every bank that issues credit cards from here to the fifth star in Orion offers at least one card capable of doing so. Just make sure there aren't any surprises waiting for you before you jump in head first.