Philosophy is concerned with the pursuit of wisdom: not only with what we think we know, but how? why? and what is it really worth? In line with this spirit of questioning philosophy can be defined as the discipline of critical scrutiny, though its specific methods are informed by a variety of philosophical styles, claims, histories, and concerns from Plato to Kant to Foucault, which constitute often quite divergent schools. Philosophers from different traditions see philosophy differently (check out the anthology of answers by contemporary philosophers to the what is philosophy question over at the excellent Philosophy Bites). But here's my take on it.
The strength of philosophy is in its open-mindedness and commitment to deep critical thinking. Its greatest weakness of course is the mirror image of its strengths: a poor sense of proportion (pursuing an argument to the point of absurdity), and irrelevance to the real world and real people's concerns (just what strange rational world did Kant live in?). In this respect David Hill has neatly described (analytic) philosophy as "the ungainly attempt to tackle questions that come naturally to children, using methods that come naturally to lawyers."
Because of this structural feature, successful philosophy requires negotiating a reasonable course through a treacherous strait. On one side lies the mundane world of sciences, arts, and common life, a world of muggles content to wallow in their own ignorance, a life-world that seems incredibly conceptually impoverished, dull and slow compared with the sparkling philosopher's life. On the other side lies the esoteric world of pure reason, a high pure realm where there is little oxygen to breathe and hallucinations are frequent.
The history of philosophy is full of occasions when philosophers did 'descend' to the mundane. The disciplines of physics, economics, psychology, computer science, and so forth all started with philosophers' questions, but as soon as people started developing small-m methodologies, with just a few fixed and unquestioned concepts, for systematically answering them, the philosophers left in pursuit of more open, concept-rich topics. All such disciplines are quite respectable in their own way, of course, but too limited to count as proper philosophy anymore.
Philosophy is far more concerned with raising questions like "How does the sun work", using clever conceptual analysis and theory construction to set them up, than in the answers, which however marvellous at first glance, quickly acquire the tedium of the mundane: "Gosh, a great ball of hydrogen under such pressure that nuclear fusion takes place? Yawn". The best questions (the ones at the core of western philosophy since Plato) are those that teeter on the edge of intelligibility - such as "How can something stay the same thing when it changes?" or "What is truth?". These are good philosophical questions because even posing them requires elegant multi-tiered conceptual constructions, and there isn't much chance of ever getting a definitive (i.e. boring) answer. The intellectual dance can continue indefinitely: incessant, addictive, inescapable, like Facebook for grown-ups. (As Wittgenstein noted, "The real discovery is the one which enables me to stop doing philosophy when I want to. The one that gives philosophy peace, so that it is no longer tormented by questions which bring itself into question.")
So philosophy is obviously biased towards the esoteric world of ideas. The first problem with this attitude is that to the extent that pure philosophy concerns itself with itself it will produce little of relevance to the world of muggles. It thus takes on the character of a private hobby whose value only its acolytes perceive. Like chess.
Secondly, that study may itself be impoverished to the extent that muggle disciplines, such as psychology, politics, and physics, are deliberately excluded as lesser forms of knowledge rather than as different and possibly complementary projects (although 'experimental philosophy' is making a comeback). It is a mistake to think that philosophy is in the meta-knowledge business: understood as independently advancing humanity's true knowledge brick by brick. Philosophy is in the understanding business, and that should include understanding and learning from the practises we attempt to criticise.
Thirdly, philosophy misses a tremendous opportunity to apply its sophisticated skills directly to the world of muggles. The specialists in operative concepts should speak up when some conceptual artist claims her work is about "resisting the system". 'Really? How? What do you mean by that, exactly? Why?' . When some economist claims that governments should concern themselves with maximising happiness it is the trained philosopher who should be there to ask what she means by happiness. To show that she is employing three different concepts of utility interchangeably in her welfare economics models (none of which seems to justify the crude income metric actually employed). To challenge sloppy reasoning: "Happiness is just obviously the most important thing?". To analyse its implications and how they may conflict with our other foundational moral commitments and values (such as respecting the distinctness of individuals). That is not to say that conceptual analysis is always helpful or appropriate - don't try analysing love with your partner - but the engaged philosopher is more likely to develop the required sense of judgement than the esoteric one.
In pure philosophy philosophers seek to impress each other by posing and critiquing elegantly formed questions, in perfect isolation from the rest of the world. Outside philosophy people try to answer questions using the tool set they already have. But the answer I suggest to 'What is philosophy?' takes the question as a practical one, and points to the applied philosophy where the critical skills of philosophers are genuinely engaged with the concerns of other disciplines (and even ordinary life), making scientists more critical, and philosophers more humble and grounded. The resources of philosophy are best engaged in considering the world, and especially the human projects and studies that struggle to understand it. That is where the strengths of philosophy shine brightest, and its weaknesses least.