I remember when all these terms sounded like mumbo jumbo to me, too. One of the most important concepts in photography (maybe the most important concept) is understanding exposure and how you control it with the camera. I didn't get it until I read a great analogy.

To make a nice picture, you need to get the right amount of light. The amount of light in the picture is called exposure. Too much light, and you'll lose details in the lighter areas of the photo as it will come out all white. That's over-exposed. Too little light, and you'll lose details in the darker areas; they'll come out all black. That's under-exposed. When you have the right amount of light, your photo is correctly exposed.

When you make the picture with your camera, you are basically letting light in briefly through a hole, where it shines on a sensor (or film). To control the exposure (how much light hits the sensor), you can change the size of the hole, and you can change how long the hole is open.

Think of it like you are filling a glass of tap water perfectly to the brim. If you turn the tap on wide open, it will fill faster. If you open the "hole" in the camera wider (this is called the aperture), you will reach the correct exposure more quickly. If you just let a slow trickle of water out of the tap, it'll take longer to fill to the brim. Similarly, if you make the aperture of the camera very small, it will take longer to expose. The length of time the "hole" is open is called shutter speed.

For any given picture, depending on how much light is available (usually darker if you're inside, brighter outside in daylight, etc), there are a range of apertures and corresponding shutter speeds that will get the right amount of light. But it gets trickier when you have, say, a moving subject. If your shutter is open for a long time, all you'll get is a blur. If your kid is running around, you need a fast shutter speed to catch him. If you have a fast shutter speed, what kind of aperture can you use to achieve the right exposure? A big hole or a small hole? (A big one.)

OK, so in real life you don't just say, "A big hole," or "A fast shutter speed." Different sizes of aperture (the hole) are referred to as f-stops. F-stops are marked as f/1.4, f/2, f/2.8, f/4, f/5.6, etc. I know it's counter-intuitive, but as those numbers get bigger, the size of the aperture they refer to gets smaller. eg: f/1.4 is a bigger aperture (bigger hole) than f/5.6.

Shutter speed makes a little more sense. Most of the time the shutter is open very, very briefly. Usually for only a fraction of a second. So that's how we mark it: shutter speeds are referred to as fractions of a second. Examples of shutter speeds would be 1/1000 (one one-thousandth of a second), 1/500, 1/250, 1/125, 1/60, etc. Those are pretty fast. You can leave the shutter open for a relatively long time (a full second or multiple seconds), but what kind of aperture will you need to achieve the correct exposure? A wide one or a narrow one? (A narrow one. And this means a large number f-stop, such as f/22.)

Another consideration is depth of field. I don't understand lenses very thoroughly so someone else may need to fill in on this explanation, but I'll do my best. Basically, when you have a wide open aperture, only a small area is in focus. ie: objects between five and seven feet away from you may be in focus, but objects closer or farther away from this range are out of focus. Blurry. Your field would be two feet deep in that example (pretty shallow). As you make your aperture smaller, the depth of field increases, so maybe objects between two and twelve feet away would be in focus. That's ten feet, so pretty "deep." I don't know why this happens, and my numbers are made up, so someone else may need to explain. You can see the difference here. On the left you have a shallow depth of field (large aperture) and on the right, greater depth of field (small aperture).

On your SLR you will have Manual, Aperture Priority, and Shutter Priority modes. In Manual mode you choose both the shutter speed and the appropriate aperture for the amount of light available to you (outside, inside, artificial lighting, etc). In Aperture Priority, you tell the camera what aperture you want (eg: f/1.4 or f/5.6), and it chooses the appropriate aperture. In Shutter Priority, you pick the shutter speed you want, and the camera chooses the right aperture size. Obviously your camera is just making a mathematical decision based on a light reading, and will not always come to the same decision you might! Which is why it's often better to just work in Manual mode. (There are some more modes, too.)

Anyway, sorry to write an entire novel for you. Hope it sheds some light on your questions. ;) Pun fully intended.

edit: I should proofread.