What does differentiation mean and represent? (A-Level students)

Simply put, differentiation allows you do find the gradient of a line, whether it is linear or a curve. When you first learn about the equation of a straight line, commonly displayed in the form y=mx+c, where m and c are constants, the m represents the gradient of this line. To work out the gradient of a straight line you only need two points on that line. From there, you find the difference in the "y" values and divide that by the difference in the "x" values and therefore can be shown as dy/dx. This shows the amount the "y" value increases/decreases when you move along by one unit in the positive "x" direction and hence, the gradient of the line. dy/dx is also used the find the gradient of a curve, however this is a little bit harder as calculus is involved in working this out. However you can use this to find the stationary points on curves (where the gradient/m/dy/dx = 0) and is therefore very useful in many ways.