The shutter sits directly in front of the sensor on most cameras. It's job is to open and close very quickly to expose the sensor to the light entering through the lens. Shutter speed is the amount of time that the sensor is exposed to light. The sensor is usually exposed to light for a very short period of time. In order to get one more stop of light you must double the time that the shutter is open. In order to go down a stop (aka cut the light in half) you must also cut the shutter speed in half.
Shutter speed is easy because the way we measure it is exactly how you would think. We use the time that the shutter is open. Usually it's given as a fraction of a second. For example, 1/125 or 1/400. This means the shutter is open for 1/125th of a second or 1/400th of a second. This is way faster than our brains can register. If our eyes were video cameras our shutter speed would be 1/24th of a second. This is one reason photography can be so amazing. It can capture moments we can't see with our own eyes because they happen faster than we comprehend.
Shutter speed determines motion blur and camera shake. Motion blur is cause by movement in the scene. The faster the shutter speed, the less motion blur. In the picture below notice that everything is in focus except his left hand. That's because everything is static except that hand. Because he was moving and my shutter speed was not fast enough to "stop" his motion I ended up with motion blur.
There is not a certain shutter speed that stops all motion. For example, if I'm taking a picture of a tortoise a shutter speed of 1/100th of a second might be fast enough to eliminate motion blur. However, if I'm trying to shoot a 200 mph race car, then a shutter speed of 1/8000th of a second might not be fast enough to eliminate motion blur. It very much depends on the subject. This is something that you need to experiment with and figure out how fast your shutter must be to stop motion. If I'm shooting a motionless person I never shoot slower than 1/50th. If I'm shooting people that are walking and moving around I don't shoot slower than 1/200th of a second. But both of those are the slowest shutter I use. If I had the choice I would shoot almost everything at the maximum shutter speed of my camera (1/8000th). Unfortunately, the only time that's an option is when I'm shooting in direct sunlight, and no photographer wants to shoot in direct sun all the time.
The other reason shutter speed is important is camera shake. When we are holding a camera in our hands it's not perfectly steady. The camera is always moving a little bit. That movement can cause your images to blur. The slower the shutter speed, the more this is exaggerated.
In order to eliminate motion blur and camera shake, we want the fastest shutter speed possible. Remember that.
I'll keep adding to the blog, but for now go take some pictures!