Things that have depth and can be rotated in space are three-dimensional. Everything around you that you can touch or move around—your sneaker, your dog, the rug on the floor—is three-dimensional.
Dimensionality can be a tricky quality to understand, but it helps to think of a line connecting two points as one-dimensional and a flat plane or shape, like a triangle drawn on paper, as two-dimensional. When you add depth to a shape, you get a three-dimensional object: a triangle becomes a pyramid, for example. When a story or other work of art is so well-made and detailed that it's believable, you can also describe it as three-dimensional.