Sensitivity is also called "ISO" or "film speed", which are much more commonly used, but are somewhat less descriptive. There is also the now-antiquated "ASA" just in case you needed more jargon rattling around in your brain.
Just to set the record straight, "ISO" refers to the International Standards Organization. Its not a unit per se, but just an agreed upon convention about how sensitive a photographic medium is (such as film or a digital image sensor). ASA is the old school American Standards Organization, which actually uses the exact same scale as ISO, it's just different letters. So ignore that crap.
As far as film speed goes, when you are dealing with film, its sensitivity is a fixed property engineered into the film. You can't change it, you can just change which film you are using. Since most of us are shooting digital, at least most of the time, it's important to know that you CAN change the sensitivity of a digital sensor with just the press of a button.
So what is sensitivity? Do we have to watch LifeTime movies now? Bravo? No, fortunately we don't.
Sensitivity is how easily a digital sensor (or film) reacts to light. If the sensitivity is high, it takes less light to get a correct exposure. If the sensitivity is low, it takes more light. As mentioned above, sensitivity is most commonly given as an ISO setting. Here's a progression of ISO settings, all one full stop apart.
100, 200, 400, 800, 1600, 3200
Notice something familiar? The number doubles or half when moving from one setting to the next. Just like aperture and shutter speed, sensitivity operates in "stops", but this time we aren't changing the amount of light allowed in the camera, just how the image sensor reacts to it.
Let's go back to the ever-exciting water analogy. If aperture is the width of the hose, and shutter speed is how long its turned on, sensitivity is the size of the bucket we are trying to fill. ISO 100 is a kiddie pool, ISO 1600 is a coffee cup.
Another familiar example of sensitivity is sun burn. Some people are fair-skinned and burn to a crisp in 30 minutes. They are ISO 1600. Other people are dark as night and take all day to get burned. They are ISO 100. Get it?
ISO, just like aperture and shutter speed, has other important affects on your photography, especially regarding image quality and noise. We'll circle around for that shortly when we get into the creative uses of ISO, but first we'll start applying what we've learned about exposure.