64 bits versions of Windows have many folders and data structures separated for running 32 and 64 bits programs together, side-by-side. In particular, "Program files" and "Program Files (x86)" is one of those.
The purpose is the same as it always was, to serve as the standard place to install system-wide software. As x64 Windows is fully capable of running both x64 and x86 programs, it must be also possible to install them at the same time. So it was created the notion of having two program files folders for each one, to serve each as the standard based on the bitness.
But its whole existence is merely to serve as a convention, as everything it does can be solved by other means. There is no limitation that programs must be installed to the "proper" folder according to its 32/64 bits status, Windows simply doesn't cares at all about the location. The main advantage is to make it possible to have both versions of a program installed simulaneously, something that most default configurations of Windows do, and most software out there respect that convention. But in the end, it's just that, a convention.
Could one of them be deleted?
Yes, absolutely. The location of each is fully configurable and can even be changed to the same location. As long as you consolidate them in one place, you can get rid of the other.
Shoud one of them be deleted?
I can't think a good reason for even attempting doing so. All I said in the previous paragraph is possible, but terribly difficult to do in practice, and there isn't even any benefit in doing so, so why bother? This convention is one of the rare cases where the defaults in Windows not only works well, but also makes sense and are a good idea.
