A flexible tube is clamped into place and continually massaged in one direction from the outside. This is usually done by a few cams, or by a single cam with several nubs.

While peristaltic pumps are not very efficient or powerful, they are favored for use in medical devices because they do a good job with viscous fluids, and they keep the icky stuff separated from the greasy stuff, without introducing anything that can cause a stroke.