Wetted area is a shorthand way of describing all the surface area of a piece of airplane structure exposed to airflow.
If you think about the hydrodynamic roots of aerodynamics, it would correspond to area of a ship's hull below the water line.
In the case of a winglet or raked tip, the added wetted area would be the sum of the areas of upper and lower surfaces and the tip fairing.
The wetted area includes the curvature of the surface, not just the projected planform area.
As you might suspect, wetted area is directly related to the skin friction drag of the component.