The shutter in a camera is the thing that moves when the shutter release button is pressed exposing the camera sensor to light. 

Shutter speed is the amount of time that the camera sensor is exposed to light. The shutter speed can be changed to allow more or less light to reach the sensor, getting a correct exposure in combination with the aperture and ISO. Fast shutter speeds freeze the action and capture fast-moving things, and are also used in bright lighting conditions. Slow shutter speeds can create movement and blur in photos and are also used in low-light conditions. 

When taking photos handheld the shutter speed needs to be fast enough to prevent camera shake and ensure that you get a sharp image every time.