making an exposure is like filling a bucket

If you use a garden hose to fill a bucket with water, it might take a little while. With a fire hose, it'll take considerably less time to fill the same bucket.

In making an exposure, a certain amount of light is allowed to reach the sensor/film by some combination of aperture and shutter speed.  Think of size of the aperture as the hose size, and relate shutter speed to the amount of time it takes to fill the bucket. With a small aperture opening, it takes longer to let in a certain amount of light (slower shutter speed).  On the other hand, with a larger aperture opening, it'll take less time to let in the same amount of light ( i.e., a faster shutter speed).

If you switch to an aperture that's twice as big, it will take only half the time.  If you use an aperture that's half as big, it will take twice as long. Pretty straight-forward, isn't it? This give-n-take relationship is sometimes called reciprocity.  For example, for an exposure f/5.6 at 1/60s, we could get the same exposure by using f/8 at 1/30s. (The aperture opening at f/8 is half as big as f/5.6)

This was an Aha! moment when it finally made sense to me.  For a given lighting situation there are many different combinations of aperture and shutter speed that will give the equivalent exposure. Which one to use?  Why, it's completely up to you!  Is shallow depth-of-field more important?  Then pick a large aperture opening.  Is creating motion blur more important?  Then pick a combination that will give you a slow shutter speed.

The following seven images were shot using this idea of equivalent exposures. At first glance, they all look pretty similar.  However, notice in the first image at f/2.8, the foreground leaves are out of focus, but becomes increasingly clear as we go towards f/22.  Also at 1/60s, we can make out the water and the bubbles pretty well, but at 1 second of exposure, the waterfall and bubbles become a nice and blurry.  This, my friends, is the secret sauce.

 f/2.8, 1/60s

 f/4, 1/30s

 f/5.6, 1/15s

 f/8, 1/8s

 f/11, 1/4s

 f/16, 1/2s

f/22, 1s

I've somewhat purposely left out ISO, which is another factor that affects exposure. Strictly speaking, ISO is not part of the exposure, the total amount of light hitting the film/sensor. The higher the ISO, the higher the "sensitivity" and thus the less light you need to achieve the same exposure. Think of higher ISO as a smaller bucket to fill, if you will.