Just like rotary cutting, you need three components (plus fabric) to cut shapes.
A fabric cutter (which works similarly to an old fashioned laundry mangle or pasta maker), a cutting die and a mat. Each die has very sharp steel blades that form the shape to be cut; the sharp edges are surrounded by foam so that you can run your hand over the die and not be hurt.
To use the die, lay your fabric covering the blades foam side up, then lay a mat on top of the fabric and pass through the rollers on the cutter.
The pressure created by the rollers causes the blade to push against the mat, cutting your fabric between them.