The bottom line is that the sound is due to a helium pump that disperses liquid helium in order to cool the wires that control the magnets down to -269.1 degrees Celsius. MRI machines work by generating a very large magnetic field using a super conducting magnet and many coils of wires through which a current is passed. Maintaining a large magnetic field requires a lot of energy. By cooling the wires with liquid helium down to as close to -269 degrees Celsius as possible, the resistance in the wires is almost zero allowing for highly efficient maintenance of a high magnetic field. A typical MRI scanner uses almost two tons of liquid helium.
On a related note, check out this video of what happens inside a CT Scanner!