Machine Learning is the theory and implementation of computer algorithms that improve as they are exposed to more information or data. It’s a subfield of Artificial Intelligence and Computer Science.
The process of learning is the process of improvement by gathering and processing information. There are many different types of learning. A learner can be given direct information from a teacher, which it then interprets (or understands) to perform better at some task. Learning also happens through experience, either through trial and error, or through actively interpreting those experiences in order to improve.
The merger of learning with machines means finding algorithms that automate this process. Because the inputs come in the form of data, statistical models are usually a key foundation of machine learning algorithms.
Machine learning algorithms differ from other types of algorithms in that they can improve over time. This is not possible with non-machine learning algorithms which either remain the same, or in the case of complex software will degrade over time as maintenance is required.
Note that machine learning algorithms are not immune to this degradation - if for examples the data coming in (often called the training data) becomes less helpful in solving the problem under consideration. Especially prone to this are algorithms that are trained using machine learning but not longer updated.
Relationship to Bayesian Inference
Machine learning and Bayesian inference are often linked together. Although machine learning algorithms can be written without using bayesian inference, or without using a bayesian framework, the statistical methodology of inference provides a principled way for machine learning algorithms to update and select their models after being exposed to more data.