Intercepts are points where a line or curve crosses an axis on a graph. In a two-dimensional coordinate system, there are two main types of intercepts: the x-intercept, where the graph crosses the x-axis, and the y-intercept, where it crosses the y-axis. These points are important for understanding the behavior of functions and equations. To find the x-intercept, set the y-value to zero and solve for x. Conversely, to find the y-intercept, set the x-value to zero and solve for y. Intercepts provide valuable information about the graph's position and can help in sketching the overall shape of the function.