I don't know why psychologists named the subject I care most about arousal, but it makes every speaking engagement more entertaining.
Arousal is the subjective feeling a person has that relates to intensity. When a person is excited, anxious, nervous, angry, frustratrated, etc. their arousal increases. This increase in arousal changes how we perceive the world and our behavior. For example, if I'm bored in class (low arousal), I may not be able to pay attention to my teacher or focus on my readings.
Name almost any emotion concept and there is usually an arousal component. So by measuring when and how arousal changes, we can better understand the emotional experience that an individual is having.
If you want to read and understand the theory of arousal more, I suggest you read a paper I wrote on the subject for my Emotional Theory class taught by Dr. James Russell:
Theoretical Paper on Arousal - Provides a Strong Overview
What is Electrodermal Activity (EDA)?
EDA is a measurement of how open your sweat glands are. These sweat glands are tied to the sympathetic nervous system. The sympathetic nervous system can best be though of your fight or flight response, it activates as a person prepares for action (think of adrenaline rushing or your heart rate increasing). When the sympathetic nervous activates, we can see clear increases in EDA. As a person becomes aroused (see above), often times, the sympathetic nervous system becomes activated too, so EDA can indirectly show us a person's arousal. This video explains EDA in a more visual manner.