The shutter of your digital camera allows light to enter onto the image sensor to create an image. The shutter speed determines how long the shutter stays open, and therefore how much light is captured.
Shutter speeds are measured in increments of a second, such as 1/60 or 1/250. As well as increasing the amount of light captured and thus effecting exposure, shooting with a slower shutter speed leaves you more susceptible to capturing blurry images, both from subjects in your frame moving and small movements of your hands causing camera shake.
Understanding the effects of different shutter speeds can obviously be used to your advantage. If you are photographing a fast-moving subject that you wish to be captured still in your photograph, you will need to select a fast shutter speed. Conversely, if you wish to emphasise movement, which is popular in waterfall photography, your best bet is a slower shutter speed. If you are using slow shutter speeds however, a tripod is necessary for negating camera shake.