A popular use with regression is to predict stock prices. This is done because we are considering the fluidity of price over time, and attempting to forecast the next fluid price in the future using a continuous dataset.
Regression is a form of supervised machine learning, which is where the scientist teaches the machine by showing it features and then showing it was the correct answer is, over and over, to teach the machine. Once the machine is taught, the scientist will usually "test" the machine on some unseen data, where the scientist still knows what the correct answer is, but the machine doesn't. The machine's answers are compared to the known answers, and the machine's accuracy can be measured. If the accuracy is high enough, the scientist may consider actually employing the algorithm in the real world.