The term "analytic philosophy" in part denotes the fact that most of this philosophy traces its roots to the movement of "logical analysis" at the beginning of the century; in part the term serves to distinguish "analytic" from other "kinds" of philosophy, especially "continental philosophy." The latter denotes mainly philosophy that has taken place on continental Europe after (but not including) Kant. One term indicates a method of philosophy and the other indicates a range of subject matter; and the "distinction," prevalent as it is, reflects painfully many inaccuracies: Frege, Wittgenstein, Carnap, the Logical Positivists (the Vienna Circle), the Logical Empiricists (in Berlin), and the Polish logicians were all products of the continent, and were as analytic as it is possible to be. Much philosophy in Germany today, most of that in Scandinavia, and a great deal scattered over the rest of the continent, is likewise "analytic." Conversely, "continental philosophy" is pursued throughout the United States, although often just in literature departments.
There are many who now claim that the distinction is worthless: none of the subject matter of "continental philosophy" is incapable of being studied using the traditional tools of "analytic philosophy." If this is true, the phrase "analytic philosophy" is just redundant (or maybe normative, as in "rigorous philosophy"), and the phrase "continental philosophy" (like "Greek Philosophy") just denotes a certain historical period or series of schools in philosophy: German Idealism, Marxism, Psychoanalysis, Existentialism, Phenomenology, and Post-Structuralism.
The split between the two began early in the twentieth century: the logical positivists promoted a systematic rejection of metaphysics and a general hostility to certain metaphysical concepts that they considered meaningless or ill-conceived: for example, God, the immaterial soul or universals such as "redness". This was at the same time that Heidegger was dominating philosophy in Germany and France, and his work therefore often became the object of derision in English-speaking philosophy departments. Analytic philosophy, in the end, failed by its own lights ever to systematically demonstrate the meaninginglessness or fictitiousness of the concepts it attacked--at least, few analytic philosophers today would agree that they have anything like an exact and proven theory of which terms are meaningful and which meaningless--and contemporary analytic philosophy journals are--for good or ill--as rich in metaphysics as any continental philosopher.
It has led to a number of successes: modern logic, recognizing the primary importance of sense and reference in the construction of meaning, Kurt Gödel's Incompleteness Theorem, Bertrand Russell's theory of definite descriptions, Karl Popper's theory of falsificationism, Alfred Tarski's Semantic Theory of Truth (others worth mentioning?).