Analytic philosophy was a philosophical movement of the 1900s. It hard (impossible?) to define, but basically it was a revolt against the vague and flowery metaphysics that were abound at the time. It was especially against absolute idealism (AKA objective idealism). This was close to Berkeley's Idealism, the main difference being the addition of holism. Along with this, the common 'wild metaphysical speculation' held that things like beauty were objective, and that reality could only be know through reason.

Analytic philosophy goes in for careful definitions and inspections of the parts of your arguments. (Reductionism or Logical Atomism). It likes experience over thought (Empiricism over Rationalism). It has also spawned Logical Positivism (AKA Positivism, see Verificationism, Verification Criteria of Meaning)

Some philosophers who were analytic philosophers: G.E. Moore, Bertrand Russell, A.J. Ayer, Gilbert Ryle, John Wisdom, Willard van Orman Quine, P.F. Strawson, and Hilary Putnam.
Analytic philosophy is still 'in' today, although not as strong as it once was.

Below is my original WU. It is true, it is good, it was just not enough. Analytic philosophy is many things.

One theory of the best way to conduct philosophy.

A method of conceptual analysis in philosophy in which you analyze your intuitions to find truths. For example, to find out what is 'right', you would find a concept of 'right' that you think sounds complete. 'Right is giving everyone as much freedom as possible' Then you (or others) can test it in as many theoretical situations as possible. Even one possible situation which your intuition doesn't like the way things work will call for a modification of the concept. 'Hitler would use this freedom to kill millions of people'. And so you modify it.
And this goes on until the concept is perfect.

This system doesn't work too well, because everyone has different intuitions of what might be ment by any one term. And so, we have come up with Naturalized Philosophy and Revisionary Philosophy*.