But what is it actually like to use? Well, it's pretty pleasant. Just go to the Profiles tab, pick your region, realm, and character name, and away you go. You can save any profile for future quick reference from the "my profiles" drop-down in the top-right. I encounter a short (15 second) queue to refresh my character from the Armory, and then was presented with all kinds of useful information. Here's Skosiris's page, for example.
Similar to sites like WoW Heroes or Be Imba, Wowhead assigns a gear score for each character. This takes into account the quality (ilvl) of your items, enchants, and gems. The gear score is color-coded for quick reference: white, green, blue, or purple (an orange score is theoretically possible, but it would take a gear score of 4,000). This could be a good reference for checking on unfamiliar characters, if it's weighted well.
The other information is all standard stuff, although it's very well presented. You can see a player's progress in achievements on the Normal and Heroic modes of the various raids, as well as how many of each kind of Emblem they've looted. A gold border around a raid's icon (like Naxx-10 and OS-10 in the screenshot) indicate that the character has cleared the raid. The default Armory panes ("Base," "Defenses," etc.) with all your character's stats are broken out for easy reference below that.
It also shows a brief version of a character's talent spec (0/55/16, for instance) on the front page, and if you want more, switch on over to the "Talents" tab, which loads pleasantly fast. It also shows glyphs, and gives easy access to both of a character's specs if they are dual-specced.
The Reputation and Achievements tabs are similarly well laid out and easy to use. It took me a few minutes to figure out that you can click an achievement category to view achievements in that category, and I think the Wrath reputations should be listed first in the rep tab, but those are minor complaints.
As for being able to save profiles and edit them, that seems to be working pretty well, although there are still a few bugs to be ironed out. You can easily equip gear in a slot by name (right-click on the slot and click "Equip"), and then save characters with talents and sets of gear as whatever you want. Profiles can be public or private, so you can link them to your friends or keep them all to yourself.
You can also put your characters in the witness protection program - anyone who figures out the real realm and character name of my druid wins one internet. (Offer void if you're in my guild.) Edit: We have a winner! Good job, ctrlfrk.
Anyway, slight bugs aside, the Wowhead Profiler is an excellent addition to the site, and a huge jump ahead of any other profiling tools I've seen. Great work, Claire! And if you have any questions about the profiler, you can probably find the answers on the extensive help page.