Focal length is the most obvious way in which a lens affects a photo: it controls the angle of view, and hence how much of the scene is included in your photo. The reason that it is measured in focal length rather than degrees, is that the angle of view yielded by a certain focal length depends on the size of the camera's image sensor.
So doubling the focal length is just like cropping the photo to half of its width and height and blowing up the result to full size, except without the loss of resolution that would occur if you did that in Photoshop. Everything else about the picture remains exactly the same.
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A landscape at 18mm, the white box marking 1/5 of the width and height | The same landscape at 90mm: the focal length is 5 times longer so the area marked by the white box fills the whole scene |
Shutter speed
The shutter speed is considered an exposure setting because opening the shutter for twice as long lets in twice as much light which increases the exposure of the whole scene by a stop. However you can also use it aesthetically: faster shutter speeds freeze a moving subject, slower speeds record a motion blur. Neither is 'correct': a photo of a stream with a 1/800 second shutter would record each sharp sparkling droplet of water frozen in mid-air, whereas a 4 second exposure would render the stream as a softly flowing ethereal smoke. Either can look beautiful.
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A shutter speed of 1/800 second freezes this baseball in mid-air. | A 10 second exposure produces streaked lines of headlights and a ghost of a car that was parked for half of the exposure. |
Aperture
Lenses have an aperture to control the amount of light entering them. This is an iris that can open and close to allow more or less light in. Aperture is measured in 'f numbers' – written f/x where x is the ratio of the aperture width to the focal length. Low f-numbers mean wide apertures letting in more light. Aperture has a reputation for being complicated so some guides suggest that you just memorize the f-number sequence and ignore the internal details. Being a geek, you'll find it much simpler when you understand why it is measured like this.
The first supposedly confusing thing about aperture is that it is not measured as a width but as a ratio of focal length to width. This makes more sense if you consider that the scene you're photographing is a light source. Recall that doubling the focal length will half the width and height of the bit of the scene that you project onto the camera plate. Therefore at double the focal length, only 1/4 of the scene area is providing light, so the aperture area must be 4 times as large to compensate (i.e. the aperture width must double). A constant f-number means a constant amount of light entering the aperture regardless of the focal length.
The next supposedly confusing thing about aperture is that the f-number sequence goes in stop increments: 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32. There is a logic to this. A 50mm lens with a 50mm aperture will have an f-number of f/1 (the ratio of the focal length to the aperture diameter: 50/50 = 1). If you want to halve the amount of light reaching the sensor you must halve the area of the aperture. To half the area of a circle you divide the diameter by 1.4 (give or take), and since diameter is the denominator in the f-number equation, this means that the f-number is increased by a factor of 1.4. Each f-number is 1.4 times the previous one and lets in half as much light. When someone says "close", "reduce" or "step down" the aperture, they mean increase the f-number.
Like shutter speed, aperture affects the look of the photo, specifically the depth of field. At narrow apertures the whole of a scene will be in focus, whereas at wide apertures only the bit of the scene that you focus on will be on focus; as is clear in the case of these cheap fake flowers:
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At f/16 the background is distracting | At f/1.4 the background is reduced to a blur, but not all of the subject is in focus either. |
ISO is a measurement of a digital camera's imaging sensor's sensitivity. Digital cameras with high ISO capability are better able to take low-light images and pictures of fast moving objects.
Superior Sensors: DSLRs typically use a sensor that is approximately the same dimensions as an APS film negative (22.7 x 15.1 mm). In contrast, the 2/3" sensor size of an 8 Megapixel digicam is dramatically smaller, about the size of the tip of your pinky (8.8 x 6.6 mm). The larger sensor translates directly to higher image quality in terms of detail, color depth, and dynamic range.
Less Noise: Noise is the digital equivalent of film grain. The fact that DSLRs display less noise is at least in part a result of the larger sensor size mentioned above, however it is significant enough to warrant getting its very own bullet point. With your typical digicam, you will get noticeable noise which is detrimental to image quality at pretty much anything above the lowest possible ISO setting. Contrast that with your typical modern DSLR, where you can actually make acceptable prints even at some of the highest ISO settings. I should note that in the literal sense, DSLRs usually make MORE noise when you click the shutter than a point-n-shoot, hehe.
Accessories Galore: DSLR cameras can almost be considered upgradeable, they have so many accessories... There are lenses, filters, adapters, extension tubes, flashes, strobes, brackets, and the list goes on. For example, you can buy affordable general purpose lenses or high-end lenses with superior quality. Some lenses serve special functions as well, such as those with image stabilization, macro abilities, tilt-shift functionality, and soft focus. You get the idea. With a DSLR, you have a lot of compatible tools at your disposal which opens the door to new creative possibilities.
No Shutter Lag: Shutter lag is that awful delay between the time that you click the shutter on a digicam and the time that an image is actually taken. With DSLRs, there is virtually no delay between the time that you click the shutter and the image is taken. How many times have you missed a great photo opportunity because the camera didn't focus fast enough and then didn't take the shot fast enough once it was focused?
Instant Startup: Most DSLRs have nearly instant startup times. That means if your camera is hanging around your neck and in the OFF position, and you see a three-legged man riding a unicycle towards you, you can quickly turn the camera on and snap the shot. And the aforementioned lack of shutter lag will further help in getting the photo. With a digicam it will usually take several seconds to startup, and then you'll have to wait a second or so for it to focus, and then when you click the shutter there will be maybe another second before the image is actually taken - and the three-legged man will be gone.
Higher Build Quality: Most digicams are plastic, plastic, and more plastic. They feel flimsy and they're not all that hard to break. DSLRs are built to much higher standards, increasingly so as you get into the more expensive models of course. Some of the cheaper DSLRs are still going to have a lot of plastic in them, but overall they're more 
Viewfinder: This can be a plus and a minus, but mainly it's a plus. With a DSLR, you do not compose your shots on the camera's LCD, you do so through the viewfinder, and you're actually looking through the lens (that's what TTL stands for, though not to be confused with TheTechLounge). Looking through the viewfinder allows you to see more detail as you compose your shots with regard to what's in focus, and you won't have to worry about glare on an LCD interfering with composition. The only negative looking through the viewfinder really has is that if you are in a situation where you have to shoot from the hip or over your head, you have to sort of blindly shoot. By contrast, some digicams have swiveling and rotating LCD screens which allow you to compose such a shot without a problem. It's a small sacrifice. I suppose there's also the fact that it might be less comfortable to press your face against the back of the camera, but you get used to it.
Ergonomics: Back when I used to shoot with a small digicam, I would notice that my hand would cramp after a while of holding the tiny camera. DSLRs are larger and have molded grips which (to a varying degree) make holding the camera for long periods much more comfortable. The cheaper DSLRs are smaller and less comfortable, whereas the more expensive ones are usually larger and more comfortable. This is actually the main reason why I chose to purchase a Canon 20D over a Canon Digital Rebel XT - the 20D feels much better in my hand. And since I'm on the computer 
Price: DSLR cameras are practically affordable nowadays. The big two (Canon and Nikon) currently offer DSLRs for as low as $500-$600 (Canon Digital Rebel XT and Nikon D50) and they've been encroaching on point-n-shoot price territory more and more each year. Believe it or not, this is actually already cheaper than some digicams out there. Not to mention the fact that you can often find a great deal on a used DSLR at some major online stores 
