Those dimensions are the horizontal and vertical pixels. When you crop you are removing pixels from the image so those numbers will get smaller. The ratio of those two numbers will be correct for the size image you want to print. If you crop too much, you will have problems printing to large prints with good results.
It is kinda like zooming in, but think of it as digital zoom. You get closer but the printed image quality will start to diminish at a point.
As for just cropping to a certain aspect ratio you can usually keep one of the numbers the same. So your going to loose some of the image off one of the sides. I know in lightroom I can set the crop tool to a certain aspect ratio. Drag it out to the edges of the image. That gives me the least amount of crop for any given print size of that ratio.
You don't HAVE to crop your pictures to print them in diferent sizes however it is sometimes a good idea to do so since somewhere between your camera and the print the image will be cropped to fit the aspect ratio of the print you ordered. Do you want to decide what goes, or do you want some computer/tech doing it for you.