Support vector machines (SVMs) are supervised machine learning models that analyze data used for classification and regression analysis. SVMs find a hyperplane that separates clusters of data points and maximizes the margin between the different classes. They can be used for applications like credit card approval predictions, patient risk assessments in hospitals, and categorizing text and web pages. SVMs work by finding the optimal separating hyperplane that maximizes the margin between different classes of data points in the training set.