When you think of slope you measure rise and divide by run. So if you have two points and , then the average slope is
So the difference we label with the Greek symbol delta
Now consider the points becoming closer and closer together. The deltas which are finite are replaced with infinitessimals dy and dx and then you have the continuous slope is
So in some sense you can think of these things as discrete differences in the limit of them approaching a continous change.
Hope this helps