Answers to Why is there a maximum humidity? address the thermodynamics of water vapor in air, and the Earth Science SE question How is relative humidity determined from a wet and dry bulb readings? and its answers address how a wet/dry bulb hygrometer works and how to convert the readings to a relative humidity (RH).
Usually the wet bulb is a few degrees C cooler than the dry bulb, and when they read nearly the same temperature (which happens more frequently than I'd like where I live) you know the RH is approaching 100%.
What would happen if I put a wet/dry bulb hygrometer in supersaturated air (RH > 100%)? Would the wet bulb's temperature pass through the dry bulb's and end up reading hotter than the dry bulb's temperature?
From the Earth Science SE question How is relative humidity determined from a wet and dry bulb readings? To get a numerical value for humidity with this set up you use the coarse table on the front (there's a finer table on the back of the box) and look up the dry bulb temperature and the dry minus wet difference to find an approximate humidity. For example If I look up 19 and 2 °C for those respectively (roughly what's shown in the image) I get about 81% relative humidity.