It means "the derivative of y with respect to x" where y is a function of the independent variable x! That's probably what you learned. If you are looking for something deeper it is "the rate of change of y relative to x". How fast y changes as x changes. For example, if y is a constant, the it doesn't change so \(\displaystyle \frac{dy}{dx}= 0\). If y= x, y changes exactly as fast as x so \(\displaystyle \frac{dy}{dx}= 1\). If y= 5x then y changes 5 times as fast as x (if x changes from 1 to 2, y changes from 5(1)= 5 to 5(2)= 10 so changes by 5, 5 times as much as x) so \(\displaystyle \frac{dy}{dx}= 5\).
For linear functions, all that is very easy and can be done with algebra. For non-linear functions it is not so easy. For example, if \(\displaystyle y= x^2\) and x changes from 1 to 2, y changes from 1 to 4 so has changed by 4- 1= 3 while x changed by 1. y changed by 3 times as much as x. But if x changes from 2 to 3, y changes from 4 to 9. y has changed by 5 while x still changed by 1. Now, y has changed by 5 times as much as x. The "rate of change of y compared to x" is, for y a non-linear function, a function of x rather than a constant. That is the situation where we need "Calculus".
pka, I am not shocked by the question. I have known many students who learned the "mechanics" of Calculus without actually learning the "meaning". Jeckshirauw is, at least asking that question!