The distance formula is a mathematical equation used to determine the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and is expressed as d = \sqrt(x_2 - x_1)^2 + (y_2 - y_1)^2, where (x_1, y_1) and (x_2, y_2) are the coordinates of the two points. This formula is essential in various fields, including geometry, physics, and engineering, as it helps in calculating straight-line distances. By applying the distance formula, one can easily find how far apart two locations are, which is useful in navigation and mapping.