Creaks are noises in your bicycle that show up when it is ridden. Creaks can range from unnoticeable up to highly irritating.
Creaks can be hard to track down and resolve. Primarily this is because creaks may only appear while you're riding and the bike is under load. If you put the bike in the stand, it doesn't creak because there is no load.
Also, while riding, creaks can appear to come from somewhere completely unrelated to the real cause.
The main cause of a creak is subtle movement between two parts that aren't supposed to be moving.
Press-fit bottom brackets are renowned for going creaky after a while. Other common causes are pedal threads and bearings, dry bearings anywhere, bearings that are chewing up a retainer, and crank/BB spindle interfaces.
Saddles, saddle clamps and seat post clamps are causes of creaks too, but they always "throw" their noise so can be hard to pinpoint. While riding, try bouncing a little on your saddle and see if the creaks can be made to come and go, to help isolate the causes.
Stem and bar creaks are not uncommon too. You can diagnose these by twisting and pulling on the bars while stopped, because it's too risky to do this while riding. Plus if your steering gives way it's a guaranteed crash. Quill stems can generally be tightened, but threadless systems need more care.
Finally one other cause for creaks is a frame that has a crack developing. Wash your bike and look at it all over under a strong light, looking for cracks in the frame. If you find anything suspicious then get it checked by an LBS.
Also, a creaky bike makes other riders/pedestrians look at you funny, which is to be avoided.