Wet skimming means your skimmate is literally more wet. Depending on your skimmer you will set it to skim wet or dry differently, but in general you raise the warer level or increase the bubbles.
When skimming wet, you are taking out more stuff. This is a pro and a con at the same time. You are taking out more pollutants, but can also be taking out other things. Skimming out saltwater can change your salinity over time. Skimming dry is being more selective. The percent of waste in your skimmate is higher, but your overall amount of skimmate is less.