Think of it like a water hose with the aperture being the circumference or the girth of the hose. A larger aperture, bigger water hose, (smaller number like f/1.4) allows more light in while a smaller aperture, like a straw, (larger number f/16) lets in a smaller amount. A larger aperture allows the exposure to be made in a shorter amount of time (a faster shutter speed like 1/180) while a smaller aperture takes longer amount of time to get the same exposure (a slower shutter speed like 1/60).
If you take a meter reading of a scene and the light meter tells you that a proper exposure could be made with an aperture setting of f/8 and a shutter speed of 1/180, you can achieve that same picture by increasing your shutter speed 1 stop and decreasing the aperture 1 stop and still have the same exposure value of 0 (or 2 or 3 or x stops as long as it is proportional or vice versa). This knowledge allows you to change the depth of field (DoF) for a portrait (having a larger aperture like 2.8) and blur the background while keeping the subject in focus. It will also allow you to create images like freezing action (with faster shutter speed) or slowing action like making a water fall smooth and 'wispy' with a slower shutter speed.
The third variable is the ISO which changes the sensitivity of film (or sensor) to light. A lower ISO like 100 will decrease the amount of noise or grain but makes it less sensitive to light and therefore forces you to use slower shutter speeds in low light (sometimes making it vulnerable to camera shake and motion blur). Higher ISO like 800 is more sensitive to light (allowing for higher shutter speeds when you can't lower the aperture any more due to lens limitations) but introduces more grain/noise.
So, the ISO, aperture, and shutter speed all are inter-connected.