Using an uploaded combat log(/combatlog in-game) pulled from your WoW folder, WWS parses it into a neat and clean report for your perusal. Right at your fingertips is your basic overall damage meter and healing meter, and if you dig a bit further, there's so much more. With the ability to see each boss encounter and attempt individually, each players' spell usage, the buffs and debuffs on a character in any given encounter as well as a variety of other things, this is a tool that shouldn't be overlooked if you're in the raid game.
I wouldn't recommend using this tool simply as a glorified damage meter. Its always fun to see how high(or low) you are on the DPS chart, but WoW Web Stats supplies far more information and insight than just what your damage will tell you. This is something to keep in mind if your raid is trying out new recruits. For example, using the Abilities breakdown to compare the spell rotation of your seasoned vets versus your recruits will tell you a little about how much they know about their class. For tank recruits, you may want to keep an eye on Omen during the run for their threat output in addition to the WWS report afterwards; TPS is something WoW Web Stats doesn't cover.
Personally, my favorite part of WoW Web Stats is looking at player deaths, and what dug their grave. Counting how many times the shadow priests killed themselves with Shadow Word: Death never gets old. Not that we DO that or anything. Really now, who knew you weren't supposed to cast that during Enfeeble? Our raid leaders also get a kick out of searching WWS reports for various upcoming bosses- they're sorted in order of highest DPS to lowest. Perfect for your inner min-maxing powergamer!
I don't think a full tutorial of how to use the various facets of WWS is necessary, but its worth noting that to get the most accurate readings from this tool, you'll want to increase your logging range. It can also be pretty rough trying to remember to turn combat logging on every time you enter a raid, so I suggest picking up an add-on like Auto Combat Log which will do it for you automatically.
A special thanks goes out to Mr or Ms Anonymous, who submitted the idea for this post at the exact same moment I had it myself. We're soulmates, hooray!