In geometry, a tangent is a straight line that touches a curve at one point. At the place where they touch, the line and the curve both have the same slope (they are both "going in the same direction"). For this reason, a tangent line is a good approximation of the curve near that point. The curve and the tangent line are almost exactly the same near the intersection point.
Tangent lines are useful in calculus because they can magnify the slope of a curve at a single point. The slope of some curve at the point P is often called the instantaneous rate of change of the curve at P. The instantaneous rate of change at a specific point on the curve can be found by evaluating the derivative function for the curve at that point.