Machine Learning is the science (and art) of programming computers so they can learn from data.

A more formal definition:

It is the field of study that gives computers the ability to learn without being explicitly programmed. Arthur Samuel, 1959

A more engineering-oriented definition:

A computer program is said to learn from experience E with respect to some task T and some performance measure P, if its performance on T, as measured by P, improves with experience   E. Tom Mitchell, 1997

Source: “Hands-On Machine Learning with Scikit-Learn and TensorFlow by Aurélien Géron (O’Reilly). Copyright 2017 Aurélien Géron, 978-1-491-96229-9.”

Machine learning (ML) is a field of computer science which spawned out of research in artificial intelligence. The strength of machine learning over other forms of analytics is in its ability to uncover hidden insights and predict outcomes of future, unseen inputs (generalization). Unlike iterative algorithms where operations are explicitly declared, machine learning algorithms borrow concepts from probability theory to select, evaluate, and improve statistical models.