String theory has been quite debatable over the years, especially in the Big Bang Theory. It's cool because Leonard Hoffstader and Sheldon Cooper talk about this many times and I finally know what they have been discussing about.
String Theory is basically the idea that in our three dimensional world, particles are strings/membranes that can connect to each dimension. The way that physicists can determine whether string theory is true or not, is for them to develop a telescope that can zoom in by a thousand, maybe even a million times more than what our modern telescopes can do to see these small particles. This probably is impossible to happen but who knows..