What do Minecraft gift cards do?
I know you can get gift codes for Minecraft. I haven't heard of cards, but if they do exist, I'm sure they have nothing more than a similar gift code on them. This may be to enable people without credit cards to easily buy a premium Minecraft account.
Just for the sake of comprehensiveness, a gift code allows you to upgrade a free Minecraft account to a premium one.
However, as @lunboks stated, this is the first I've ever heard of this. You may have gotten gift card confused with gift code.
The current answer is a tad outdated, hence me answering this question.
Gift codes are twelve characters and can be used to upgrade a non-premium Minecraft account to a premium one. You can do that here. However, this was the only way to purchase Minecraft, other than pay for it normally, one year ago.
Now, gift cards have been released. Some kids have expressed to Notch that their parents don't trust online paying, so Mojang has released the gift card. Gift cards can be bought at Target, Best Buy, and so on in the United States for the same amount a normal premium account can be bought with. Gift cards include a code on the back of the card, which one can use to upgrade their existing non-premium account. It also makes giving the code to a friend easier if you see them in person, since you don't have to email the code.