Libertine

Since it's what I study in university, I'll try and answer the question.

As a starter, though, it is important to know that it is commonly accepted that the meaning of the term is too controversial to accurately define.

Let's begin by looking at the etymology. Of course, the etymology is actually misleading, but it does serve an important purpose. Philosophy stems from the Greek philos and sophos, meaning "love of wisdom". Although that is certainly not its meaning, the term stems fromt the pursuit of wisdom rather than possession of it. The roots of philosophy, therefore, lay in searching for knowledge rather than clinging to dogma.

Western philosophy started with the Ancient Greek natural philosophers, who are by many considered to be the ones who first started trying to examine and analize the world in a rational, critical, fundamental way. They tried to explain the first causes of the phenomena witnessed in nature by applying critical thought, observation and deliberation to them, searching for a coherent whole behind the matter rather than believing in existing dogma and folklore.

Over the ages, philosophers continued this work, seeking to find rational frameworks, fundaments, etc. to see the world in. Their efforts were concentrated on a vast array of subjects, such as ethics, the good life, politics, the human mind, metaphysics, knowledge, ontology, logic, etc.

At the core of philosophical though, however, is a dedication to rigorous application of reason. A philosopher, or at least a good one, will never stop his inquiries somewhere along the line and say "and that's just the way it is". Everything is subject to inquiry and criticism, including the very methods or even possibility of inquiry and criticism. No argument is accepted, or at least should be accepted, without good reason.

Contemporary philosophy can be divided into a number of branches, although these necessarily spill over into eachother:
- ontology (essentially studying the nature of being)
- epistemology (essentially studying the nature and possibility of knowledge)
- metaphysics (the study of first principles, ontology, etc)
- philosophy of science (how science should work and how it does work)
- ethics
- political philosophy (in most cases prescriptive)
- philosophy of mind
- logic and semantics, which are closely related to...
- philosophy of language
- aesthetics
- cultural philosophy
- the history of philosophy
... and I'm undoubtedly forgetting a bunch of important ones.

Philosophy is NOT, however, mysticism, dogma, occultism, personal outlook on life, religion, etc. Although, in some cases, it does touch on these issues (ethics touches on outlook of life, etc).

Essentially, you can probably see philosophy as that science which concerns itself with those things that do not fall into other branches of science and are not purely empirical. Most importantly, it is based on reason, critical though, and the relentless pursuit of strong arguments that can not be determined purely by empirical observations.

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