Cycling your tank is the process of building up beneficial bacteria in your tank (on rock, sand, everything really). This bacteria is necessary to break down Ammonia (fish waste products) into nitrite, and finally nitrate. Ammonia is very deadly to fish with nitrate being the least harmful etc. Ideally, you want to be cycled before you add any fish,coral, or inverts into your tank. See the article above.
Cycling time can vary depending on if you're using live rock/sand, how big your tank is etc. Some can cycle in a few days to more than 6 weeks.
Hope this helps.