What is the basic reason for step mashing?

The temperature steps relate to enzymes as has been mentioned before. For mashing the important enzymes are alpha- and beta-amylases. Alpha cuts large chunks (dextrins) off of the starch that is in suspension in your mash. Beta cuts small bits (disaccharides, mostly maltose). Those large chunks are hard to digest for the yeast, the disaccharides are easy. Alpha works best at ~70C, beta works best at ~62C (and is pretty much inactivated at alpha's favourite temperature). The way I see it, is these enzymes are like smart, little machines that sort of just come with the malt for free. They perform very specific tasks and all we need to do, is to decide which tasks are important for us in the beer we want to make and then switch the respective machines on. And the way to that, is to heat the mash to their favourite temperature, provide contact between them and the starch (e.g. by stirring) and give them time to do their job. So by chosing your temperatures and times smartly, you can influence how much of your extract is "yeast food", turning mostly into alcohol and CO2, and how much of your extract makes it through to your beer in form of malty taste and mouthfeel.

There is enough overlap in enzyme temp ranges that a step mash doesn't make a world of difference. I keep doing them to see if I can convince myself that there's a valid reason to do it, but I have yet to see enough difference to really warrant a step mash. That overlap can be seen in the following chart from How to Brew by John Palmer.

Different families of enzymes do their thing at different temperatures. Mashing at differnt temperatures will apparently result in a wort with different properties than keeping it at the same temp for the whole mash time.

For example, apparently dextrins add body to beer, but don't add taste. Dextrins are formed at higher mash temps, so beer from a mash that spent very little time above 64 degrees (celcius) ought to have less body than one from a mash done entirely at 66 degrees.

It's a very complicated subject which I wish I understood much better. But in a nutshell, varying your mash times and temps is going to vary the properties of the beer you end up with.