| Possessing all three spatial dimensions -- length, width, and height -- plus a fourth dimension of time. A four-dimensional object changes its three-dimensional shape over time. You exist as a four-dimensional being, growing and moving through all three spatial dimensions as time passes. (However, the time dimension is unique in that we can only move through it in one direction -- unless you count memory as a way to move "back in time".)
In a mathematical context, "four-dimensional" typically refers to four spatial dimensions -- the three which we are used to, plus an abstract and imperceptible fourth spatial dimension. A hypercube is the most popular and easy-to-understand four-dimensional geometric shape. When a four-dimensional object is rendered on a computer, it is usually depicted as a three-dimensional object which changes shape over time, and which always possesses the same three-dimensional shape at a particular time index. | 
