Stands for "American Standard Code for Information Interchange." ASCII is the universal standard for the numerical codes computers use to represent all upper and lower-case letters, numbers, and puctuation. Without ASCII, each type of computer would use a different way of representing letters and numbers, causing major chaos for computer programmers (allowing them even less sleep than they already get).
ASCII makes is possible for text to be represented the same way on a Dell Dimension in Minneapolis, Minnesota as it is on an Apple Power Mac in Paris, France. There are 128 standard ASCII codes, each of which can be represented by a 7 digit binary number (because 2^7 = 128).