I was doing a comparison of phantom 4 pro and Mavic Pro 2. The only difference I can tel is the phantom has mechanical shutter. Does anyone know what does it do?

Firstly, mechanical shutters are only applicable to still photos, not video.

A mechanical shutter will tend to have fewer artefacts when shooting fast changing subjects. This may be a fast moving object in the image or banding caused by certain types of artificial lighting.

In my opinion, this is not a big deal in a drone.

No but a camera that is not glued in to its holder is.