It refers to the Nitrogen Cycle and it's the process of building up a population of beneficial bacteria to take care of the toxic ammonia that fish produce.
When you set up a new tank everything is nice and clean and there's no bacteria. As the tank ages the bacteria begin to populate the system, in the gravel, on ornaments but mainly in the filter media. That's what the black balls are for, to give the bacteria a home, although there are better medias IMO, porous ceramics mostly. The bacteria consume ammonia, which is extremely toxic to fish, and convert it to nitrite, which is less toxic but still toxic. Another bacteria starts to populate the system next which converts the nitrite to nitrate. Nitrate is tolerable to fish in small amounts and we control it with waterchanges, preferably 30-50% weekly. The whole cycle can take 6-8 weeks and at the start waterchanges can sometimes be necessary on a daily or two daily basis, depending on whether there is any detectable ammonia or nitrite. A test kit is needed to confirm their presence.
There's heaps of info about it on the 'net. Here's just one, http://www.worldcichlids.com/faqs/cycling.html but Google will give you tons of sites to look at and a search of the forum will help you too HTH