When starting to sweat under your arms, you can sometimes feel it dripping down and you have no control over where it is going.
Wearing an undershirt underneath whatever you are wearing will control the sweating by making it all sink into the shirt and not going anywhere else. Although, if you are an excessive sweater, your sweat will just go trough what you are wearing over it. So, the suggestion is to wear something a bit lose on top of it. For example, having an open, comfortable long sleeve shirt over it is perfect as you can show your undershirt, have a chilled and cool style, AND get some air under you arms.