From my understanding bicubic and bilinear, etc. refer to the number of pixels taken into account around a given pixel when reconstructing or changing an image. You can think of it like a grid that is used to rebuild a new image, similar to compression.
If for example the application is going to reconstruct an image at a smaller size (using fewer pixels) it examines the data to determine what will be thrown out, what will be left, and what will be averaged. So say you have a blue pixel surrounded top bottom left and right by red pixels which in turn are sitting in a field of white. The resampling mode determines if the app looks only at the blue pixel and what is immediately next to it, or whether it looks beyond to the pixels surrounding the red ones as well. This will determine if the reconstructed image contains a single purple pixel as a result, or a purplish blue pixel with some bluish pink antialiased pixels around it etc. Chances are the different results will be too subtle to really notice. I always leave it checked to the default.
