If you're new to fishing and just heard of leaders, you've probably asked yourself why you'd ever want to tie a different kind of fishing line to the existing line on your reel/rod. Recently, I wrote about the three main types of fishing lines and the advantages and disadvatages of each. Using a leader allows you to capitalize on the advantages of both line types.
One of the most common unions I use is a fluorcarbon leader joined to braid. Braid is a great line, with zero stretch and high abrasion resistance. However, it's highly visible in the water column and this will often spook fish in clear water. Using a flurocarbon leader allows me to capitalize on braid's strengths while not spooking fish as bad in clear water.
There are several leader combinations that are effective. It would likely take a few full length articles to cover them all. If you're a seasoned veteran this isn't news to you. However, if you're newer to fishing, I highly encourage you to look into using leaders. It'll give you the advantages of multiple line types and you won't think it's as funny as it seems when you give it a try.