We're all pretty familiar with the first three dimensions -- after all, we experience those dimensions daily as we move about our world. But scientists and mathematicians have long gone three dimensions using thought experiments, conceptualizing a fourth dimension -- and of course, to many more dimensions beyond. You may have heard of the fourth dimension via Madeleine L'Engle's A Wrinkle in Time, which mentioned the tesseract, a four-dimensional "hypercube." In L'Engle's work, the tesseract had properties that could bend space-time, though a real tesseract would simply be an object in four-dimensional space. Anyway, let's not get carried away with tesseracts just yet. I stumbled across a wonderful video of Carl Sagan explaining the fourth dimension in a way that anyone can understand. He explains dimensionality as a notion, expanding from a two-dimensional "flatland" to our three-dimensional world, and onward to the fourth dimension. The video is only seven minutes long -- have a look:

Neat, huh? See also: Flatland: A Romance of Many Dimensions, a sci-fi story from 1884.