This sound is produced by the vibration created by the wet skin of the finger on a very clean wine glass rim. You can easily do this yourself on any glass. Make sure that your hands are clean and that the glass is clean.

Wet your finger with wine or water (not spit) and very lightly and smoothly move your finger around the rim. Increase pressure slightly and at some point the glass will begin vibrating. This is just the friction of your skin against the glass and the motion causing your finger to stop and start very rapidly as it is dragged across the glass. At resonant frequencies you can hear the sound. (The resonant frequency for a glass is changed by the amount of liquid in it, so that is why the glasses are filled with different amounts.)