It seems that the answer to that question varies depanding on who is asked, which is fitting, since one of the more tongue in cheek definitions is that philosophy is questions that cannot be answered. A few definitions from famous philosophers can be found at Wikiquote.
According to Webster, Philosophy is "all learning exclusive of technical precepts and practical arts." I have to confess that this definition does not satisfy me, it even seems somewhat absurd. Webster then gives a second definition: "the sciences and liberal arts exclusive of medicine, law, and theology." This seems to complicate things a little more.
Define.com gives the more common definition of Philosophy, "Literally, the love of, inducing the search after, wisdom." This definition can be found on many web sites and even in many text book introductions to philosophy. While technically this definition is not wrong, as it is the translation of the word from the Greek, I find it almost impossible to explain what love is, and what wisdom means. Furthermore, love of wisdom does not really explain that philosophy is an analytical process.
One of the best definitions I have seen is at definition.com. They define Philosophy in part as "the rational investigation of the truths and principles of being, knowledge, or conduct." I like that definition because it is tight and direct. It uses the word 'rational' which to me is the essence of what philosophy is. The only objection I have to this definition is the use of the word 'truths' and to a lesser degree of the word 'principles'. I believe that the notion that there are 'truths' has not been demonstrated and believe further that some of those 'truths' can never be known.