Recipe says "brown lamb chops in oil", when it says brown them, what's that mean? Just make the outside brown?

This step will also produce something called a "fond"- basically material that sticks to the pan. This is generally rinsed off the pan with liquid- wine, water etc. in a step called "deglazing" and used as an element of a pan sauce or gravy, or otherwise included in the finished dish.

You heat the oil in a skillet at a fairly high heat & cook the chops on each side until they are brown. This adds flavor. You normally aren't cooking the chops completely, just searing the surface, but that depends on your recipe