In the time it takes for you to finish reading this, you have traveled without moving.
Even while not moving in what we perceive as fixed space, we have moved forward along the fourth dimension; time.
We live in a world of three dimensions. Well, we only perceive three dimensions. We can hypothesize many more dimensions. But, they are difficult to imagine.
Because of Einstein, we often call time the fourth dimension. Special relativity shows that time behaves surprisingly like the three spatial dimensions. The Lorenz equations show this. Length contracts as speed increases. Time expands as speed increases.
Scientists have been graphing time, as if it were a length, for hundreds of years. To the left is a typical graph, showing two things in motion at the same speed, one to the left and one to the right. Time never behaves exactly like a spatial dimension. You cannot go backward in time. And you normally cannot go forward at different rates. But, there are surprising parallels. For some purposes, it is handy to call time a fourth dimension. For other purposes, it is not.
More: http://www.jimloy.com/physics/4d.htm
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