Mines extract minerals from the planet's core. The four minerals are neutronium, tritanium, duranium, and molybdenum. The planet screen lists a density for each of these minerals; this is multiplied by the number of mines to determine how many units of each mineral are mined in any given turn. Certain player or native races may further modify this.
If you build a great number of mineral mines, the population on the planet will become unhappy and you will be forced to drop the tax rate to keep them happy or else face the risk of riots and war. (Refer to Taxes and Happiness for more information on this.) Mineral mines and factories risk showing up on enemy sensors unless the planet has more than 15 defense posts.