Is diopter adjustment necessary for a digital camera? How does it work? The sony DSC V3 doesn't have this feature but its LCD screen is very bright, and has vivid colors. If sony remove this option , would it cause the user to miss the target of the shot?

A diopter doesn't change a thing about the camera. It changes how you see things when looking through the viewfinder. It's a corrective vision tool. For some people diopters are necessary.

how does the diopter work? I wear eye glasses. I prefer to use the LCD screen because it has better resolution and display actual objects.

If the LCD screen is on the back of the camera, then you don't need a diopter adjustment.
You only need the adjustment on a view of an internal LCD (Minolta A1, A2, Z1, Panasonic FZ20) because that involved magnifying lenses and focussing on a tiny screen.

The diapter adjustment is necessary for me when I look through the viewfinder of an SLR (I wear glasses). Otherwise, things look out of fucus when actual focused. It has nothing to do with the LCD preview.