In simple terms, the aperture is a hole which can be opened or closed to control the amount of light reaching the camera sensor. The wider the hole, the more light is let in (helping compensate for darker conditions, for example). Remember, the smaller the f/number, the wider the aperture.
Every lens performs better at some f/numbers than others. Generally, you will see the image resolution & contrast deteriorate at the end of the f/number spectrum. To determine the optimum aperture for the lens you own, find a piece of paper with fine printed type (eg. the financial pages or a Bible). Set up your camera to photograph the page straight on & frame it to fill the viewfinder. Now set the camera to AV mode & take pictures working your way through the apertures. Load the images onto your computer & view them at high magnification. You should see a gain in resolution & contrast as you close the aperture down from maximum & then a drop as you approach the smallest apertures.
On the lens I have which came with the camera (a Canon EF-S18-55mm) f/13 appeared to give the best results.