Rawr is a Windows program which will download your character from the armory and use a database of WoW gear, enchants, gems, consumables, and other enhancements to suggest gear upgrades, better gemmings, and other ways of improving your performance in WoW.
To get started, go to the website and download the zip file of the latest version. Use your favorite unzipper to extract the files into a convenient directory. There is no installer. Just unzip and run rawr.exe.
Once rawr is running, go to the File menu and select Load From Armory. Enter the information for your toon and wait a moment while rawr downloads your toon.
On the left side of the rawr window, you'll see all of the gear your toon is currently wearing, along with its gems and enchants, surrounding a text area showing your stats. The text area has tabs showing your talent spec, the buffs you want to use in calculations, and an options panel for configuring fight assumptions. On the right side, you'll see a list of gear with numbers and bars.
First off, make sure that the Stats panel has the correct Model selected. For Al, it starts off with Healadin selected, so I have to switch that to Retribution, otherwise nothing else will make sense. After a bit of recalculation, the right panel now shows a list of helms with blue bars to the right of them indicating how much dps each item would contribute to my overall dps, based on all of the other configured items.
If you look above the bars, there are three pulldown menus -- Gear, Sort, Filter. The default sort is Overall, but I'm raid dps, so I want to sort purely on dps, not based on the total value of the items including health and other factors not directly increasing my damage output. You can use the Filter pulldown to eliminate from this list items you don't want to consider. For instance, if you don't do PvP, you can uncheck PvP as a source of gear.
In the gear list you'll see the same item listed more than once, with different dps (or hps) values. If you mouse over the items, you'll see that each instance of the item is showing it with different gems socketed. To give you an idea of how important correct gemming is, my Spiked Titansteel Helm can vary from 104dps incorrectly gemmed to nearly 142dps correctly gemmed. (You should NEVER show up to a raid with empty sockets. If you can't afford the 5g for green quality gems with appropriate stats, you can't afford the repair bills.) When you look through the list, you'll probably also see that the best gems for your spec will often ignore socket bonuses.
One of the really handy features of rawr is what I think of as the shopping list. If you open the Gear pulldown, near the bottom of the list you'll see Direct Upgrades. When you select that option, rawr will spend some time thinking about all of the available gear as compared to all of the gear you have equipped. When it's finally done, and this can take a little while, the window will show a list of all the gear upgrades available, sorted from biggest upgrade to smallest. Are you wondering if you should buy your T7 gloves now or wait a week to buy the T7 chest? See how much of an upgrade each of those pieces represent by looking at this list, if they're upgrades at all.
There are lots of other options and features you can tinker with, including changing your talents around while keeping your gear as it is to see how that would affect you performance. Rawr has models for tanks, healers, and dps.