This is the total distance for which the river water is in contact with the bed and banks at a given cross section. It represents the friction that slows down the river velocity, so the longer the wetted perimeter, the more friction between channel and water.
Wetted perimeter can be measured using a heavy chain, rope, or measure tape, which should be stretched across the riverbed from one bank to the other. This can be hard to do, especially in larger channels or where the bed is very rough. It is often better calculated from, the graphed results of the profile.