A memory stick is what a digital camera uses for file. When you take a photo, your camera writes it to a memory stick.
The "stick" itself is a small card-like memory device that goes into a digital camera. There are basically two types, SmartMedia and Compact Flash. Both are good, but you'll have to get the kind that your camera takes. It's usually either one or the other.
Here's a Compact Flash type card (enlarged):
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