Machine Learning is a branch of Computer Science that is concerned with designing systems that can learn from the provided input. Usually the systems are designed to use this learned knowledge to better process similar input in the future. Machine learning can be considered as a subfield of Artificial Intelligence.
A very familiar example is the email spam-catching system: given a set of emails marked as spam and not-spam, it learns the characteristics of spam emails and is then able to process future email messages to mark them as spam or not-spam.
The technique used in the above example of email spam-catching system is one of the most common machine learning techniques: classification (actually, statistical classification). More precisely it is a supervised statistical classification. Supervised because the system needs to be first trained using already classified training data as opposed to an unsupervised system where such training is not done.
A supervised learning system that performs classification is known as a learner or, more commonly, a classifier.
The classifier is first fed training data in which each item is already labeled with the correct label or class. This data is used to train the learning algorithm, which creates models that can then be used to label/classify similar data.
Formally, given a set of input items, X = {x1, x2, ... xn} and a set of labels/classes, Y = {y1, y2, ... yn} and training data T = { (xi, yi) | yi is the label/class for xi }, a classifier is a mapping from X to Y, f(T, x) = y.