Parametric equations are a way to express a set of related quantities as explicit functions of one or more independent variables, often called parameters. Instead of defining a relationship between x and y directly, parametric equations use a third variable, typically t, to describe both x and y in terms of t. This approach is particularly useful for representing curves and motion in a more flexible manner. For example, the motion of an object can be described using parametric equations where x(t) and y(t) represent the object's position at time t. This method allows for easier modeling of complex shapes and trajectories, such as circles or ellipses, which can be difficult to express with standard equations.