Mineral water is merely water that has had minerals like sodium, potassium etc added to it. The addition of the minerals could be natural, due to the water flowing through rock (or whatever) that is rich in minerals, or it could be regular water that has had minerals added in a factory or whatever. Ordinary tap water also contains minerals, although at different levels to mineral water (depending on where you live...).

As Big Daddy said, bottled water is usually "cleaned up". However, if you are concerned you can check the label on the bottle, it will tell you exactly what minerals are in the water and at what concentration. You could also try asking the bottling company, I'm sure they will give you all the information you need about purity and cleanliness.