What is it
The gauge is the number of stitches and rows required to obtain a given size (usually 4"x4"), working with a specific yarn and hook size.
Why is it important
We will probably never say it enough, making a swatch to check your gauge is crucial when making most crochet project, espacially when sizing is important. This is how you can be sure that the final size of your project is right. Not everyone crochets the same (some loosely, some thightly), not all yarns are a created equals, a lot of people don't use the yarn used in the pattern, and not all hooks (even with the same size number) are exactly the same. To make sure that your final project has the right measurement, you must make a swatch to check your gauge.
Where to find the information
Patterns should alway include gauge information at the begining. If gauge is not not crucial for the pattern you are using, there should be a note to that effect.
How to make the swatch
Always make your swatch bigger that the gauge information indicates, and measure a section in the middle. If you have the gauge to obtain 4"x4", you might want to make your swatch 5"x5".
Most patterns will include a hook size (sometimes listed in the materials section), but think of this as an indication, or a starting point only. You might need to use a different size to obtain the right gauge. You can start by making your swatch with the hook size that is listed in the pattern. If you have more stitches per inch than indicated, do it again try using a larger hook size. If you have fewer stitches per inch, then try using a smaller hook size.
If you have the right number of stitches per inch, but are not getting the right gauge for your rows, you will have to adjust the height of your stitches. You can do this by drawing a little bit more yarn (for more height), or a bit ess yarn (for less height) when working your stitches
Yes, this means that you might end up making a few swatches, but this will save you a lot of time and frustration in the end. This is still a lot better than finding out that your gauge was off when you are all done your project...many hours down the road.
How to measure
To measure your gauge, lay your work on a flat surface. Place markers 4" appart and measure the number of stitches in between, or use a gauge measurement tool.