it's how much a value is changing
if you derived x^2 (which is a parabola) you'd get 2x, which would draw a line with a slope representing how much y is increasing at some point over and at x, aka the gradient
dy/dx is just the notation for y = functions, you write it if you're not given f(x) =, for that you write f'(x)
in physics terms, if you use the equation displacement = ut + 1/2at^2 if you derived the parabolic equation of -4.9t^2 you'd get the speed at some time t by doing (2*-4.9)*t because speed is the rate of change of displacement/distance
EDIT: speed is the derived because h is the height at some point in a journey and is the y axis, and the t is time which lies on the x axis, so it's ds/dt = speed