Regression is a machine learning task where the goal is to predict a real value based on a set of feature vectors. There exists a large variety of regression algorithms: linear regression, logistic regression, gradient boosting or neural networks. During training, each of these algorithms adjusts the weights of a model based on the loss function used for optimization.
The choice of a loss function depends on a certain task and particular values of a metric required to achieve. Many loss functions (like MSE, MAE, RMSLE etc.) focus on predicting the expected value of a variable given a feature vector.