This is mine, but it looks a bit metallic or something compared to his which looks smooth. Im not sure wats wrong.
Your model is showing faces and edges, called Flat Shading, while the video shows a Smooth Shaded geometry.
Go to Object Mode, look in the Tool Panel on the 3D window (left hand panel, press T if hidden) and find the Shading buttons. Press Smooth.
It will now look like the video.