I feel that conceptually shutter speed is one of the easiest things about a DSLR to understand... after all, the name kind of gives it away! It really is the speed of the shutter! That was easy. Ok ok, obviously I'll go at a little more in depth, no worries! The shutter is what determines how long light is allowed to come into the camera and hit the sensor. This is important because it means that a slower shutter speed will allow more light, and a faster shutter speed will allow less. Now, most DSLR's have a pretty wide range of shutter speeds so it can be overwhelming deciding what shutter speed you might need. My Canon 6D, for example, has a range of shutter speeds from 30 secs. to 1/4000 sec. Crazy right?
Setting the shutter speed means understanding what you are trying to capture. For me, I'm almost always photographing portrait sessions (couples, families, etc) or weddings. Since people are generally in motion, I try and set the shutter speed so that I can capture "normal" movement & keep my images sharp, usually anywhere from 1/100 to 1/2000 sec. The faster the motion, the faster I want to set my shutter speed to be able to capture it without getting any "blur."
Again, don't forget to have fun with your own style!