It's exactly the same concept as shooting stills, but just shooting a bunch in a row to make video. Shutter speed controls how fast the shutter opens and closes to expose a frame. A slow shutter speed (i.e. 1/30) will give you slight motion blur which will create "smoother" looking video, while a faster shutter speed (i.e. 1/500 or 1/1000) will give you a more "strobing" look (the example that gets thrown around is the opening scene to Saving Private Ryan, which was shot at a high shutter speed). Just as in stills, high shutter speeds will lower the exposure of the video and slow shutter speeds will raise the exposure. People generally say to keep the shutter speed at twice the frame rate (i.e. 24 frames per second -> 1/50 shutter speed, or 30 frames per second -> 1/60 shutter speed) but you do not have to do this, often times you can "break" the rule to get the look you want! I particularly love using higher shutter speeds when shooting scenes with more action, i.e. sports, dancing, etc.
Frame rate is set through camera settings in the menu, that's just how many individual still frames per second the camera is stringing together to create video. Hope that helps.