What is differentiation in mathematics and what does it represent?

Differentiation is the rate of change of one variable with respect to another at a point in time or space. In other words, this can be described as the slope of a curve, which is how much the curve goes up or down for a certain amount of horizontal distance (Would draw a graph on the whiteboard to illustrate).

An example of this would be the speed of a car, where the speed is the distance travelled by the car differentiated with respect to the amount of time that has gone by. If the car travels 10 m in 2 seconds, it has an average speed of 5 m/s (10/2 = 5). The differentiation would provide the instantaneous speed of the car, so you would perform the same operation but for an infenitissimally small amount of time Dt.