I'm looking at a Canon 17-40 mm wide angle lens, and I don't understand why anyone would buy it. EFS18-55mm II is the standard Canon 18-55 mm lens that DSLRs come with, and it seems almost as wide – 18 mm vs. 17 mm. Does the wide angle lens have a feature I'm missing, or is that extra 1 mm worth it?
I don't understand why anyone would buy it
Optical quality, build quality, and overall durability. The EF 17-40mm f/4L USM is an "L series" lens -- essentially professional grade, while the EF-S 18-55mm f/3.5-5.6 is a consumer grade "kit" lens. L lenses are made with better materials, better designs, and more features. They're weather sealed to keep out moisture and dust. You'll notice that the maximum aperture for the 17-40mm is f/4 across the entire zoom range, whereas it varies between f/3.5 and f/5.6 on the 18-55mm. Most importantly, L lenses tend to have better optics -- sharper focus and fewer optical flaws such as chromatic aberration. Also, the "USM" designation on the 17-40mm stands for "ultrasonic motor", i.e. the autofocus motor is nearly silent yet very fast.
One other important difference is that the 18-55mm is an EF-S lens. The "-S" means "small image circle" -- lenses designated "EF-S" instead of "EF" produce a smaller image at the back end, inside the camera. For that reason, and also because EF-S lenses may project a bit further into the camera body, EF-S lenses only work on crop-sensor bodies (the Digital Rebel series, the x0D cameras, and the 7D. The smaller sensor doesn't require as large an image as larger sensors, and the smaller image in turn allows lenses to use smaller components. That means that EF-S lenses can be smaller, lighter, and less expensive than their EF counterparts. Note that the 18-55mm also includes image stabilization, while the 17-40mm doesn't.
To answer your title question, the difference between focal lengths of 17mm and 18mm is small enough that you could consider the two lenses to be about the same, focal-length-wise, when used on the same body. (On the other hand, 17mm on a full frame sensor is a lot wider than the same lens on a crop sensor. 17mm on a crop sensor gives the same effect as a 27mm lens on a full frame sensor.)
By the way, you might also want to compare the EF-S 17-55mm f/2.8 IS USM to your kit lens. The focal range on that lens is almost exactly the same as the 18-55mm, neither lens is designated "L", both offer image stabilization, and yet the 17-55mm costs about the same (a little more, actually) than the 17-40mm. How can that be? It's pretty much the same answer -- despite some similar specs, they're different lenses. The 17-55mm has a constant f/2.8 aperture, so it needs larger lens elements that collect more light. More glass means a heavier, more expensive lens even though it's an EF-S lens. If you want a similar lens at f/2.8 on a full frame sensor you need even more light and bigger lens elements, so the closest equivalents would be one of the two EF 24-70mm f/2.8L lenses, at $1800 or $2300, respectively.
The first thing worth mentioning is that the EF-s lens won't even work on a full frame camera, so it isn't an option for anyone using a 6d or up. The optical quality and barrel distortion are also far better on the L series lens. The build quality is more solid, it is a fixed volume lens, so it can be better weather sealed (or weather sealed at all for that matter). It has a fixed aperture range for the entire zoom range.
Overall, it is simply a better lens in addition to going 1mm wider. Focal length isn't the only factor and a large range of focal lengths isn't generally a strength. The 18-55 is basically a plastic toy with minimally capable optics while the 17-40 is a "real" lens, though I'll admit it is the lens I reach for least in my bag (preferring the much more expensive 24-70 f/2.8 II) but I do use it when I need those extra few mm of angle.
(Personal note, I own a 17-40 f/4L and have an old EF-s 18-55 from on my xTi, they don't even remotely compare in terms of quality.)
Assuming you are using an APC crop, the difference from 18 to 17 is a 3° wider field of view on the horizontal. On a full frame it would be a little more.
But in this case you are also paying for better glass. The 17-40mm is going to be a lot sharper and has a constant aperture across its focal range (of course it is slightly slower at f/4 vs f/3.5 wide open). It also has better build quality and weather sealing (with a front filter).
It is also worth noting that us crazy photographers will pay a lot for a few mm of focal length and good quality, check out the price on the 14mm f/2.8.
An even closer comparison is between the Canon EF-S 18-55 kit lens and the Canon 17-55 F2.8 lens. The kit lens sells for under $200, and the 17-55 F2.8 sells for about $1000. Five times the money, and nearly exactly the same zoom range.
Obviously, the price difference is not about the difference in zoom range.
For these specific lenses, the kit is much slower. While its rated at F3.5-5.6, its only F3.5 at the very end of its range, it quickly drops to F5.6. The difference between F5.6 and F2.8 is huge. The F2.8 lens has much more glass, and its much higher image quality.