But a gauge doesn't have to be a real object. A gauge can also be any way of measuring or figuring out how much of something there is—and to gauge something is to try to figure out how much of it there is.
For example, if your teacher says to the class, "Hands up if you like pepperoni on your pizza," then she's gauging the class's feelings about pepperoni: she's getting an idea of how many of you like pepperoni.
You can gauge all kinds of things by observing and paying close attention. If you don't have a watch or a clock nearby, you can gauge what time it is by looking at where the sun is in the sky. If you have a substitute teacher one day, you can gauge how nice or how strict he'll be by paying close attention to what he says and does. You can gauge your friends' moods—sad? happy? playful? bored?—by looking closely at their faces and listening carefully to what they say and how they say it.
You can even gauge your pet's mood, and gauge how interested she is in being petted right now.