Slide the point along the curve. The line touching it at exactly one point is the tangent — its slope is the derivative, the curve's rate of change right there.
Pick two points on a curve and draw a line through them — that's a secant, and its slope is the average rate of change between the two points. Now slide the second point closer and closer to the first. The secant line rotates and settles into the tangent line, and its slope is the derivative at that single point:
It's the instantaneous steepness of the curve — how fast f is changing right at x, not on average, but at that exact instant.