There are various types of memory cards, (Smartmedia, XD, Compact Flash, SD, Multimedia and Memory Stick being the common ones). Different manufacturers have chosen to use different types of cards.
Essentially they all do the same job; to store your pictures in the camera after they are taken. You can then download them to a computer using a memory card reader, or software supplied by the camera maker.
The are a few cameras at the cheaper end of the market that only store the pictures on the cameras internal memory. These are best avoided as they are very limiting. You can only take a few before you have to download them, and clear the memory.
Make sure you buy the right type of card for the camera you have chosen.