Regression is a fundamental ML 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 can go through some 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.