Milling is a cutting process performed by end mills which look a little like drill bits but can cut laterally (sideways). Here's a good introductory read about these bits: Makezine - "The Skinny on End Mills". Some end mills can also cut downwards but you might prefer using a drill press, cordless drill or rotary tool for drilling jobs.
CNC mills or manually controlled milling tables can shape loads of different materials. When dealing with metals, you'll often hear the term "machining". Routers (CNC or manual), on the other hand, are typically reserved for woodworking.
"Milling" can also refer to sawing timber into boards (as in "sawmill"), but we are not attempting that kind of milling yet.