Shutter speed refers to the length of time the shutter on the camera is open.
Correct exposure depends on shutter speed and aperture. Aperture controls how much light is allowed through the lens while shutter speed controls how long that light is left to shine on the film or digital sensor. Smaller apertures will mean slower (longer) shutter speeds to have the same amount of light hitting the sensor. Larger apertures mean faster (shorter) shutter speeds which can help avoid camera shake.
Many SLR cameras have a mode where the photographer can manually select the shutter speed. This is usually referred to as Tv, time value or shutter priority mode. In this mode the camera will automatically choose the necessary aperture value to correctly expose the picture.