A mountain bike is a bicycle that is typically used off road, which contains front suspension or full suspension.
History
Mountain bikes are an adaptation of the Cruiser Bicycle, which features a bigger, stronger frame and larger tires. In the early 80's bike companies started to develop bikes geared more toward off-terrain environments. The features of the bike borrowed from BMX Bicycles as well as Racing bicycles.
How to Chose a Bike
First choice you need to make is what kind of rider you would like to be. If you want to ride a few times a month, then its not worth buying an expensive bike. Furthermore, if you really enjoy riding, then you should and can justify spending a little more on a bike.
Next, you need to figure out what kind of terrain you live by or want to ride. For mostly flat terrain, a hardtail mountain bike (only front suspension) will be suitable. But, if you plan on riding rocky terrain, then a full suspension bike is a better choice.