Regression is a fundamental machine learning and statistical technique. It involves fitting the best curve to a set of data by minimizing the sum of errors for each point. Regression is well-known for providing continuous output. This means that regression finds the right curve to the data, and then uses it to predict a continuous numerical output.
If you've done Calculus, you may have a much better idea of what continuous means. That said, no problem if not, here's some intuition. If we're predicting a price, the price can be any possible numerical value. This is continuity.
On the other hand, discrete numbers mean that the price is limited to a finite number of numerical values, but cannot pass through all possible values. As an example, if we were trying to interpret a picture of handwritten numbers, there are only 10 possible output values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
As you can probably see from the example, classification usually deals with discrete outputs. But we won't get to that in this course.