Regression is a task of supervised learning: a regression model is fitted to map its inputs (which can be discrete or continuous) to some previously known outputs. The outputs of a regression model are continuous.
Practical problems of this kind may include tasks such as predicting real-estate prices, predicting demand for a service or a product at a particular date, but regression is also used in many other complex tasks under the hood: e.g. to predict bounding boxes in visual object detection.
Regression represents, along with classification, one of the two most fundamental supervised learning problems so most supervised learning methods are able to do regression, classification or both.