Skew-T diagrams are air balloon observations aloft (called soundings) that can tell you a lot about your atmospheric profile. Generally used in severe weather/thunderstorm situations, they are also used heavily in the aviation industries to look at winds in the upper levels. Occasionally they can also be used in the winter time for winds and temperature profiles.
Skew-T diagrams on the basic level plot 4 things: Dew point, temperature, winds, and height. And with that, I will let Charlie Phillips from charlie.weathertogether.net take over because he did a great job explaining it.
How to read a Skew-T Diagram here