It is basically what the lay-person would call Artificial Intelligence. This comes out of the general realization that the key aspect of an intelligent system is its ability to learn, i.e., to adapt and restructure its computational resources to gear them towards solving problems it commonly encounters (is trained to solve). Besides the hyper-parallel structure (i.e., neural-network) of our brains, the determining factor of our intelligence is the ability to form, adapt and restructure cognitive pathways in such a way that they are useful to solve the problems we encounter in everyday life.
So, machine learning is really about developing mechanisms that can extract useful information out of a pile of data, infer second-degree information from that, and use it either to become better at doing the same thing (extract information) or to take actions that are useful towards some kind of goal or task. In practical terms, however, machine learning is really just applied probability theory. There are tons of methods under the umbrella of "machine learning", from simple regressions (fitting curves through data), to state estimation (Markov processes), all the way to reinforcement learning (be trained to solve problems). The practical applications of machine learning mostly include pattern recognition (e.g., recognize faces in a picture, speech recognition, etc.), optimization algorithms, "programming" (not in the sense of "coding" but in its original academic sense, which is to plan the operation of a system (like a manufacturing plant or a mine) in order to optimize the results, this is the same meaning used for the word "programming" in expressions like linear programming, quadratic programming, integral programming or dynamic programming), data mining in large databases, sensor fusion (e.g., simultaneous location and mapping), and a ton of special applications in robotics and automation in general.