Co-branded cards are the result of a partnership between merchants, networks and card issuers. For merchants, co-branded products can provide multiple benefits, including but not limited to: increasing sales, attracting new customers, and bringing value to your most loyal customers.
Rewards credit cards offer some kind of "reward" - usually cash back, points or travel miles - for every dollar spent, sometimes up to a certain limit. Depending on the card, you can use your rewards in several ways.
In most cases, yes, as long as you have no balance and the annual fee (if the card charges an annual fee) is less than the value of the reward you get each year.