Evaporation cools you down. So a wet thermometer bulb is colder then a dry thermometer bulb. How much of a difference this makes depend on how much evaporation there is which depend on the temperature and humidity.
The wet bulb temperature matters a lot because us humans are better approximated by a wet thermometer bulb then a dry one. When it is hot we sweat which makes us wet. The evaporation of our sweat cause us to cool down. So the wet bulb temperature is a better approximation of how hot it feels then the dry bulb temperature. It describes why Florida feels so much hotter then Arizona even when the dry bulb temperature is the same in both places.
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