The Short Answer
It doesn't. The only one area where your console is the clear victor is playing games. Comparing the modern games console (Sony PlayStation 2, Microsoft XBOX, Nintendo GameCube, etc.) to the modern PC is pointless. They are different machines built for different things. The overlap in functionality is nice, but comparing consoles to PCs is akin to comparing a camera to a cameraphone and asking "Why does my camera take better pictures than my cell phone that also takes pictures?".
The Longer, but More Complete, Answer
Operating System
How much of your available resource pool (RAM and the like) does a PC operating system use? Windows XP and Mac OS X both require a fair amount of resources. When you start playing a game, that game only has access to the resources that the operating system isn't currently using. In the realm of PCs, what the OS says goes, and if the OS wants to use that chunk of RAM, your game of SMAC is going to slow down. There is an advantage to this, of course. You can alt-tab away from your game while it is paused and do other things. This is not the case on a console. Pieces of the operating system are either unloaded from memory or dormant as soon as a game is started. Have you ever wondered why you can't change the XBOX system time while playing Jade Empire? Now you know. All (or the vast majority of) the system's resources are made available to the game. This allows the programmer to optimize the game code. It also allows programming for a very narrow target. BioWare knows exactly how much memory is available and what can be pushed where. It certainly doesn't hurt that the configuration of components is a constant as well. You'd be amazed what you can coax out of an old video card when you know that it's the only card that will ever be used in conjunction with your game. The constant configuration of a game console also makes it less prone to crash†. Developers work with one set of drivers, and by testing a game on one piece of hardware, every hardware configuration has been tested. Such a comprehensive test is realistically impossible for PC software.
Competition
How many programs do you have running right now? I have three. Microsoft Excel, Mozilla Firefox (with seven tabs open), and Microsoft Outlook. If I fire up a game, these three programs will all be fighting with my game for the same resources. When I start Donkey Kong Jungle Beat on my GameCube, there are no AIM clients and spreadsheets with which to compete. There is only the GameCube and the game.
What Consoles Don't Have
Spyware. Adware. Malware. Viruses. These things can slow the average PC down to a crawl. Consoles don't have to deal with these problems. There are very few, if any, malicious programs written that target games consoles. Even if people were targeting consoles, it would difficult to deliver these programs. Consoles, when they do connect to the Internet, do not do so at the user's whim. They communicate very specific things, and they only send and receive very specific pieces of information. When you jump into an online bout of Halo 2, your XBOX knows what to send. It finds you some opponents, you choose a map,
and off you go.
Comparing Apples to Oranges
I don't have a cutting edge computer; it is around four years old. I can, however, still play lots of fun games on it. My PC runs Roller Coaster Tycoon, Syberia, Civilization III and Yohoho! Puzzle Pirates just fine. It also runs WinAmp, Microsoft Word, Macromedia Dreamweaver, and Adobe Photoshop; often simultaneously! Yeah, my XBOX can play Doom 3, but my PC can do so much more!
In terms of variety of functionality, longevity*, and return on investment, the PC clearly outperforms any games console.
† Thanks to Matthew for reminding me of this.
* It is my opinion that the average PC has a greater logevity than the average console because of the amount of software available. It is not difficult to find software (even games) that will run on an old computer (like mine that is four years old). It is, however, exceedingly difficult to find software that will run on an old console (like my Dreamcast that is only one generation back). The simple fact that consoles are viewed by manufacturers and consumers as throw-away goods while the PC is seen as an investment ensure that this is the case. After all, there have been very few Super Nintendo games produced since Nintendo moved onto the Nintendo 64 and the GameCube, but there are commercial products available today that will run on Windows 98 even though Microsoft has since moved on to Windows 2000 and Windows XP.
belgland says I disagree. Personally I'm a PC gamer who only recently got back into console gaming with the Gamecube after skipping the previous generation. In my opinion a well-built PC with relatively recent components will almost always smoke a console. One of the other issues is that it depends on where in the life cycle you're looking. A brand-new console really needs to be compared to the best PC you can build at the same time. As a console ages, PCs will be upgraded and consequently look that much better. Resident Evil 4 looks great on my Gamecube, but Half-Life 2 or Doom 3 (which came out a bit earlier) look much, much better on my PC. The other relevant area is that people rarely play highly processing intensive games (i.e. hardcore strategy or wargames) on consoles. You just need the right mix of hardware and software that plays to the strengths of each format.
jclast replies I agree that a top of the line PC will smoke a brand-new console, but I'm comparing your average person's PC to your average person's console. Money also becomes an issue. If I can get excellent looking and performing games from a $400 XBOX 360 and a mid-range computer for $500, why would I spend $1500 - $2000 on a top of the line gaming PC? You also only spend the money on a console once. If you want to keep playing the newest PC games, you'll need to keep ahead of the technology curve which is expensive and, in my opinion, inconvenient. So on one hand, I've got a $400 game station that will be current for at least three years. On the other, I've got a new gaming rig that ran me $1500 and I'll need to upgrade it in a year to play Gears of War? I'll pass.