Because

Imagine a secant line intersecting the curve you are looking for in two places.

Now let the distance between those places be denoted ..

Next imagine drawing the line differently so you decrease ...do this again and again and again

Eventually as you draw the line so that the line intersects the curve at ONE point...and at that point the line shares the slope of the curve...

Thus this is the derivative of a function(e.g. the slope)