Ok, the mirror is primarily used as a sighting device. Here's a good, short instructional video by Silva that covers the basics of map and compass navigation:
https://www.youtube.com/watch?v=4O8DmkAC2wI

Note that different kinds of compasses exist on the market. In general, a simple, inexpensive baseplate compass is the easiest to use with a map and the best option for learning the basics IMHO. Honestly speaking that's what I would recommend as a first choice if you're not quite sure what the mirror is used for. Maybe a Suunto A10 or equivalent, no need for anything particularly extravagant.

Mirror, prismatic and lensatic compasses have additional features and sighting aids for extra precision. However, they tend to be less user friendly as far as the basic functions and require more skill and experience to make good use of all the advanced features.

Also, many high-end compasses tend to be designed with a specific task in mind. E.g. a top-of-the-line prismatic compass is great for surveying or directing artillery fire but much less practical for general land navigation than a $10 baseplate compass.

A quality mirror compass is a wonderful tool, but only if you know how to use it effectively. For most tasks and users it's basically overkill. I love mirror compasses and I'm also very fond of my Cammenga lensatic for serious land navigation, but it's a different cup of tea. A baseplate is much easier to use for a novice and the learning curve is not quite as steep.