When we stand on hot sun, we sweat. Even when we do exercise, we sweat a lot. Sweating is related to increase in body heat (or temperature). As temperature of our body increases, it needs to be brought down.
When we sweat, our skin is covered with water droplets(they are not only water). as it gets evaporated, large amount of heat is absorbed from its surrounding. And we can feel the cooling effect.
One thing to remember is that water has very high specific heat. So even a small quantity of water can absorb a large quantity of energy can hence more effective in cooling.
So, yes they correctly say that evaporation causes cooling and that evaporation is facilitated by sweating.