A wet market is simply one that sells fresh meats and produce, as opposed to a market that sells dry goods.
Wet markets get their name because they have to be frequently washed down, and oftentimes ice is used to keep the meats fresh, when then melts onto the floor.
As an example, the seafood market in Seattle is a “wet market”. Many other cities have them too.
The issue, as Mike Honcho stated, is the selling of wild and exotic animals in these markets, which are sometimes kept live and slaughtered on site.
Without “wet markets” many people around the world wouldn’t have a place to acquire meat. Not every country has an Albertsons on every corner.