You have just so much information stored in those smaller images.
When you try to enlarge an image, you're basically pulling the pixels apart, and the program has to "guess" what is to occupy the additional space between the pixels. Most programs aren't very good at "guessing". I imagine, there are some high-end (expensive) image editing programs that are better at "guessing", than other programs, but I can't say for sure. Even then, I'd imagine the results would be mediocre, at best.

There's a Photoshop resizing tutorial here:

http://kb.adobe.com/selfservice/viewContent.do?externalId=331327&sliceId=1

The information generally applies to similar graphics programs.

As Kev has said, the information to preserve the quality of the image at a larger size simply does not exist. Using the option to resample gives the most reasonable results that can be achieved. A program may offer more than one algorithm (calculation method) to try - results can vary depending on the characteristics of the image.

jpg images have inherent compression artifacts and suffer quality loss when being saved. Best results will come with using a lossless format like bmp or tif during processing. If you must start from a jpg, convert it immediately to one of the lossless formats, process it to your satisfaction, then if you want to finish with jpg, only save in this format when completely finished. Use the least amount of jpg compression that will still give you reasonable reduction in file size.