The 'difference' is mainly in the size of the sensor (the part that records the photo). The 'full frame' sensors are the same size as a frame of 35mm film while the 'crop factor' camera's sensors are somewhat smaller. They are still a whole lot bigger than the sensors you will find in 99% of digicams though.
There are a few advantages of a larger sensor. One being that it doesn't have to pack in the 'photo-sites' too closely together, which can make for less digital noise (cleaner images). In a nut shell, bigger sensors will usually give you better image quality. Especially at higher ISO levels.
Another aspect of larger sensors is the Depth of Field. You get a shallower DOF with a lager sensor. You don't always want a shallow DOF, but it's nice to have the option.
When you compare a crop camera to a full frame camera, the full frame will give you a wider field of view...actually, the standard that we use for comparison is 35mm film cameras, so full frame being that same size is also considered 'standard'.
So let's say you have a 50mm lens and you are using it on a full frame camera like the 5D II. You are shooting a model and you have her whole body in the photo. Then you take that 50mm lens and put it onto a crop camera. Now because the sensor is smaller, it only 'sees' the middle portion of the image that the lens is projecting into the camera. The result is that you might only be able to see from her knees to her neck (if all else remains the same). In other words, the field of view is narrower on a crop camera (give the same focal length). The ratio for Canon cameras is 1.6. So the 50mm lens, when used on a crop camera, will 'feel' like an 80mm lens on a full frame.
So using a crop camera can be a PITA for wide angle shooting, but it's an advantage when shooting something farther away.
Luckily, the camera companies have made up for this, by giving us lenses with rather short focal lengths (wide angle), that will work with crop cameras.
So while the 'standard zoom lens' for a film camera or full frame camera is something like 24-70mm.....on a crop body camera, the 'standard zoom lens' is more in the range of 17-50mm.
Now, a lot of people make a big deal about the crop factor. But the truth (according to me

) is that it doesn't really matter, unless you are already used to one format. For example, if you were an avid user of a 35mm film camera, then you might have a certain expectation for a 50mm lens....and you might be surprised when you try to use that lens on a crop body camera. But if you don't have those preconceived expectations, then there is nothing to worry about. What you see is pretty much what you get....you don't have to constantly think about the crop factor.
Getting back to your issue of what lenses to buy, the important thing to know about all of this, is that some lenses are made to work with the crop cameras only. In the Canon line up they are the EF-
S lenses. So if you do plan on getting a full frame camera, in the for foreseeable future, then you might want to avoid buying those types of lenses.
In the Canon line up, the Rebel series and the mid-level (pro-sumer) cameras are all 1.6 crop cameras. This includes the 40D, 50D and the new 7D. If I was going to buy one today, I'd look at the 50D or the 7D.
There are two current 'full frame' models. The 5D (current versions is the mark II) and the 1Ds (mark III is the current one, I think). There is also the 1D (currently mark IV), which is a 1.3 crop. The 5D II is basically the same size of camera as the 50D but with the full frame sensor, it gives outstanding image quality. The 1 series cameras (1D and 1Ds) are Canon's pro cameras. They are bigger and much more robust. They are sealed up so you could use them in a rain storm. They have many features not found on the other cameras, but they are also very expensive at $4000 for the 1D and $8000 for the 1Ds (although I'm sure they can be found for less).
One difference between the different models is AF performance. The 1 series cameras have all the AF technology that Canon can think of, while the 5D II is actually behind the 7D. So if action/sports shooting is something you are into shooting, look for a camera that has top notch AF.
Switching to Nikon? I wouldn't recommend switching. Not that there is anything wrong with Nikon, but switching from one to the other is usually a wasteful, costly ordeal. Although, if I had to choose which DSLR is the best buy, in terms of getting full frame & top quality AF, I'd say that the Nikon D700 is probably it.
But the good thing about these systems, is that you can still use your 'lowly' XTi with top quality lenses, and get fantastic results.