What is the "wet" for in a "wet bar"?

It means the bar has running water, which is useful for cleaning citrus juice, various syrups, glassware, your hands, pouring liquid or ice out, etc.

Ice and water is also useful for chilling glassware for martinis, etc.

For the guy that wants scotch and water?

dont they usually use bottled water?
Wet bar makes me think of the phrase “wet your whistle”

Like PW said, it’s a small home bar area that includes a sink for washing glasses.

Cheers…Simon