Space-filling curves are mathematical constructs that map multi-dimensional spaces into one-dimensional lines. They are designed to cover every point in a given area without leaving any gaps. A well-known example is the Hilbert curve, which continuously fills a square by recursively dividing it into smaller sections. These curves have applications in various fields, including computer graphics, data indexing, and image processing. By organizing data in a way that preserves spatial locality, space-filling curves can improve the efficiency of algorithms that require quick access to multi-dimensional data structures.