What is an adjustable spanner / wrench?
Note: I'm British, so I call it a spanner, if you're American you call it a wrench. It's all the same thing.
What is it?
A normal spanner is one size, so if the nut or bolt you are trying to undo doesn't match the size of spanners you have, you're out of luck. An adjustable spanner does what it sounds - you can change the gap between the jaws of the spanner to match your nut.
They are very handy if you are working on a car with Metric fittings (i.e. using millimetres for measurements) and you have a mainly Imperial (AKA 'American', i.e. inches) equipment.
Adjustable spanners come in a variety of sizes:
How to use it
In the head of the spanner is a little spiral of metal. Use your thumb to turn the spiral one way and the jaws get further apart, spin it the other way and they close up. Easy.
You can only turn the spiral a certain amount before it stops, the jaws won't fall out if you keep turning it. Well, they might if you have a really cheap or very old one which is built differently, but they shouldn't.
If the spanner is old or very dirty and the spiral won't move, you might need to spray some oil in to the spiral area and down the gap where the adjusting shaft pokes out to be able to loosen things up. If it still won't shift, try tapping the adjusting jaw with a spanner, or the adjusting shaft if it's protruding from the body. Don't do it hard, just enough to jolt any rust that's built up to break the seal it has on the metal.
Pros and Cons
Adjustable spanners are great for odd jobs where you don't happen to have a tool of the right size, but they are more bulky than normal spanners and not as strong. If you have a nut that won't shift and you put a lot of pressure on the handle, an adjustable spanner can break before the nut loosens. In that sort of situation, it's better to get hold of a fixed size spanner of the right size for the job.
Some adjustables have a gauge on the side showing the size of the gap you've adjusted it to. This can help when setting it before putting it on the nut, but also tells you the size of normal spanner you need of you decide the adjustable isn't up to the job. The middle size spanner in the picture above has such a gauge on the side in Metric (millimetres), but it doesn't really come out in the photo.