Electronic shutter

Basically, electronic shutter allows to shoot completely silently in situations where you need it: street photography, wedding photography, making photos during presentations, etc. There are three things to mention however:

1. By default after switching over to electronic shutter the shutter sound is generated electronically even though there is no mechanical shutter movement. You can switch it off completely in Setup/Beep menu.
2. If you close down the aperture on an electronic lens you will hear aperture closing down sound when you release. It is much more discrete than shutter sound but still audible in silent environment. For complete silent shooting either shoot wide open or use completely mechanical lenses (without electronic coupling).
3. When using electronic shutter under certain types of lighting you may notice banding. It is caused by interferences between current frequencies and sensor readout speed. If you see it in your image the only way to get rid of it is to turn electronic shutter off.

In theory, there is also another use of electronic shutter: high sync speed flash photography. As the theory goes, since there is no physical curtain covering part of the sensor as a flash pops, it should be possible to sync flash at any speed, opening possibilities to overpower sun with a small flash on a bright day. Unfortunately, we are out of luck here: flash is disabled when using electronic shutter. I think the cause is the same why we see banding with certain types of light: sensor readout is in fact not instant but reads the sensor line by line (rolling shutter instead of global shutter, see this interview of Mr. Inoue from Panasonic).