A tangent line is a straight line that touches a curve at a single point without crossing it. This point is known as the point of tangency. The slope of the tangent line represents the instantaneous rate of change of the curve at that point, which is essential in calculus for understanding how functions behave. In the context of a circle, the tangent line is perpendicular to the radius drawn to the point of tangency. Tangent lines are used in various fields, including physics and engineering, to analyze motion and forces, as well as in the study of functions in mathematics.