What I do...
I am the Director of Client Performance at Search Discovery in Atlanta, GA, responsible for improving whatever my clients will let me improve. It's not as bad as it sounds - just a mix of a few things that a lot of people already do pretty well, just not in the same place at the same time.
Web Analytics
Web Analytics is what we use to understand whether the decisions we've made about how to design a web site are right or wrong. The practice helps us uncover what is happening, but more importantly, why it might be happening.
Contrary to what a lot of people believe right now, web analytics isn't a tool, just like cooking isn't an oven. Web analytics is a smart, diversely talented person looking at information and figuring out what it means. Then, that person works with specialists and makes some decisions about how to change the site to improve its performance. A web analyst isn't a "specialist" at all - to be good at their job, they need to know about a lot of things, including usability, design, the fundamentals of the business, and more. That's about as nutshell of an explanation as I can muster.
Usability
So what is Usability, then? In another nutshell, this is the practice of designing interfaces that people can use easily. Think about the air conditioner in your car. If it's easy to control and use, you don't even notice its design. If it's hard and confusing to use, you've probably already written Ford a letter.
Usability experts are people who understand how others will interpret how your web site should be used. They try to set the site up to make sure that a user has an easy time logging in, filling in their credit card information, getting directions to your office, or signing up for that newsletter. It's surprising how easily we can confuse people, and these valuable experts can really improve matters.
The trouble with usability, though, is that it is rarely accountable to post-design measurement (that is to say they are not accountable to whether web analytics says they're right or not). When those two disciplines are mixed, though, you get a great feedback loop that these experts can use to continually improve the way your site is used by visitors.
Design
Designers are the ones who make it all come together - the finished product in a nice, pretty form.
Designers, specifically graphic designers, used to be in the business of taking complex information (or things that are just somewhat hard to summarize quickly) and creating illustrations to make those things easier to understand. The venn diagram above is a great example. A good illustration can show you in 250 pixels what would take all of these paragraphs to explain.
Today, though, designers are in the business of making things look cool, making cutting-edge interactions, and creating an experiece that makes a user say, "Wow, that was slick." Think iPhone, but without the obsession on usability that Apple has.
The trouble with this is that designers sometimes make things MORE complicated where they used to make them LESS complicated. People are used to doing things in certain ways, particularly within certain verticals. People looking up insurance quotes need a similar experience, look, and feel across the various providers' sites. Designers are the ones who make your life miserable sometimes, and awesome other times. Usually, awesome comes when designers work with usability folks and are also accountable to web analytics, too.
The Rest of the Hornet's Nest
So what about search engine marketing? What about display? Email? Partnerships? IT? Product Research?
When you look at the rest of the site's operations: marketing, development, partnerships, search engine optimization, social networking, etc., I think it's best to look at these things as spokes off of the site performance hub. If a good product development team is founded around site performance, they are really just taking cues from their users, which is always the right way to go about things. Users are already telling you what to build next or improve: you just need to listen. The site performance team can tell you what's working, what's not, what we need to build, how to build it, how to market it, and more. Yes, this actually works.