If you ask your friend, "How do you feel, generally, about loaning your car to people?" your intention might be to gauge his reaction before you flat-out ask if you can borrow his car. To gauge is to measure or test.
The verb gauge means to estimate or measure, while the noun gauge is a tool you can use to make such a measurement. If you've ever seen someone check the air pressure in a tire, the instrument she used was called a tire gauge. The thickness, or diameter, of an item like wire (or the barrel of a gun) is another meaning of gauge.