This picture is a great representative I believe: http://en.wikipedia.org/wiki/File:Aq...ogen_Cycle.png
Soooo what happens is that you feed your fish and then they poo. That is ammonia, when the tank is not cycled this ammonia can poison your fish and hurt their gills.
Cycling the tank is the process of making the tank safe for your critters, it doesn't mean adding new water or anything. It has to go through a process to turn Ammonia into Nitrites and then into Nitrates.
All of these are bad for your fishies in big doses (so the amount of poo that is building up in your 5 gallon right now is bad for them. Dose that make sense?)
To start the cycle your tank has to be set up (like it already is) and then there needs to be a source of ammonia to start feeding the Beneficial Bacteria. These Beneficial Bacteria or BB is what keeps your fish safe from the Ammonia, Nitrites and Nitrates.
So you start off with one fish to produce some poo and then the ammonia will spike up (this can be stressful for you fish so we only recommend one fish while doing this) and then after about two weeks the ammonia will go down and the Nitrites come join the party! And then again, after about two weeks the Nitrates will come in and want to crash the party! After that you need to do a large water change, about 75% of the water.
Right after that big water change you now have grown some very beneficial bacteria and your tank is safe for your fish! Without this bacteria your fishies won't be very happy and they can be poisoned from all that poo they are producing. You wouldn't want to swim in your toilet after you've used it right?
I hope this helps and if I've lost you, please tell me :D