Wet Markets are markets which sell fresh fish, meat, vegetables and fruit, and some also sell various other things such as snacks, cooking utensils, clothes, etc. We've been told that they are called 'wet' markets because the floor is usually wet due to water being sprayed over the produce and floor to keep things clean. Wet markets can be found in most neighbourhoods in Taiwan, and they usually run in the mornings, although some are open during the afternoons.
We go to our local wet market roughly once a week to buy our fruit and vegetables. Here's a short video that we filmed on a recent visit to give you a feel for what Taiwanese wet markets are like: