Shutter speed refers to the speed of the shutter. The shutter speed is the length of time that your medium (Digital sensor, film, glass plate etc.) is exposed to light for. A fast shutter speed would be 1/2000th. This means your medium is exposed for 1/2000th of a second. A slow shutter speed would be 30” (seconds). This means your medium is exposed for 30 seconds.
Most DLSRs will have a shutter speed range of 30” to 1/4000 of a second. The double quotation mark in photography refers to seconds not inches.
The shutter is a curtain inside your camera. That curtain stops light from hitting your recording medium and from exposing a picture. When the shutter is not in use it is obstructed by a mirror. This mirror is on a 45 degree angle and bounces the light from your lens upwards into the viewfinder allowing the photographer to see through the lens.
When you push the shutter button, that mirror closes, the shutter curtain opens and light passes right through and hits your sensor. That classic sound you hear when taking a photo is the sound of the shutter curtain moving.
When the mirror closes, it is covering the path of light that you see through the lens. This is why when you take a picture everything goes black for a brief moment.
If you want to take a perfectly exposed image you need to change the shutter speed and aperture together. If you have a larger aperture (small number) this will let in a lot of light because the hole is so large. So you will need to increase the speed of the shutter to only expose the recording medium for a short moment. You can use the Tv and Av settings on your camera to automatically change your settings for you.