The term worsted means a lot of different things depending on where you are in the knitting and spinning world. For knitters, most commonly worsted refers to a weight of yarn, also known as medium weight yarn.
Worsted weight yarn is generally knit on a US 7 to 9 knitting needle (4.5 to 5.5 mm) and works up 16 to 20 stitches per four inches. Sometimes worsted weight refers to a slightly lighter weight yarn as well; this is why many people are pushing for the wider use of the standard yarn weight system, which will make it easier to understand what you're getting when you shop for yarn.
If you're a spinner, worsted refers to both a means of preparing fiber to be spun and a method for doing the spinning on a wheel. Worsted fiber preparation involves fibers that are basically all the same staple length and that have been combed so that they all face the same direction and are nice and straight.
Spinning in a worsted method means that you don't allow the twist into the drafting zone; the fibers are smoothed and stretched before the twist is allowed in. This makes for a slow spinning process, but it's worth it if you want a very even, smooth, lovely yarn.
Using these definitions of worsted, a worsted yarn provides firm stitch definition in a lustrous, strong and cool-wearing yarn. All that's true regardless of the actual weight of the yarn.
In spinning, worsted is the opposite of woolen yarn preparation and spinning methods.