There are lots of ways of representing colors with numbers (which is what all computers do). Most people are familiar with some form of RGB representation in which you have three numbers each of which represent the amount of Red, Green, and Blue in a picture. Another popular method is CMYK, which is like RGB except that you use four numbers for Cyan, Magenta, Yellow, and Black.
LAB accomplishes the same goal (colors = sets of numbers) as RGB and CMYK, but in a very different way. With LAB, the L represents brightness independent of color while the A and B values are sort of like positions on sliders between opposing colors.
There are two advantages that I know of for working with LAB. First, you can adjust L to make brightness adjustments independent of the color channels. Second, adjustments in LAB are more perceptually linear. That means that if you change an LAB value by a certain number, the corresponding visual affect changes by about the same amount, regardless of where you are on the number scale.
I don't think, unless things have changed, that Photoshop Elements has a LAB (or CMYK) mode. I think that's one of the Photoshop only features. I don't think anyone uses CMYK for anything but publishing. It is (or was - I may be out-of-date) the standard for printing books and magazines. LAB is much more useful but still not something I would consider a must-have photo editing tool.