Here are four nice definitions published on the philosophy department homepage Victoria University (Wellington, New Zealand) philosophy department website.

I especially like Campbell's thought that "philosophy is thinking in slow motion. It breaks down, describes and assesses moves we ordinarily make at great speed" because it evokes the intense practical significance of philosophical questioning, analysis, and investigation.

Wittgenstein's definition evokes the power of philosophy, although he famously (and correctly!) came to believe that the quest for "sharp boundaries" was ultimately futile and so concluded that philosophy is not as powerful as he had thought. Still, even if it often or perhaps necessarily fails, the attempt to clarify what is cloudy and indistinct is nonetheless vital.

Warnock's definition highlights the precision and critical thinking that is such a hallmark of good analytical philosophy. Studying philosophy is by no means the only way to acquire these sort of profound critical thinking skills, but it is a powerful method and arguably a uniquely powerful one.

Finally, Russell's discussion of liberation from dogmatism through philosophical questioning and doubt rings true to me: this is a reason why all students in higher education should benefit from the opportunity to acquire philosophical skills.

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Philosophy is thinking in slow motion. It breaks down, describes and assesses moves we ordinarily make at great speed - to do with our natural motivations and beliefs. It then becomes evident that alternatives are possible [John Campbell, Philosophers]

Without philosophy thoughts are, as it were, cloudy and indistinct: its task is to make them clear and to give them sharp boundaries. [Ludwig Wittgenstein, Tractatus Logico-Philosophicus]

What is the aim of philosophy? To be clear-headed rather than confused; lucid rather than obscure; rational rather than otherwise; and to be neither more, nor less, sure of things than is justifiable by argument or evidence. [Geoffrey Warnock, Philosophers]

Philosophy, though unable to tell us with certainty what is the true answer to the doubts it raises, is able to suggest many possibilities which enlarge our thoughts and free them from the tyranny of custom. Thus, while diminishing our feeling of certainty as to what things are, it greatly increases our knowledge as to what they may be; it removes the somewhat arrogant dogmatism of those who have never travelled into the region of liberating doubt, and it keeps alive our sense of wonder by showing familiar things in an unfamiliar aspect. [Bertrand Russell, The Problems of Philosophy]

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For more, see http://www.vuw.ac.nz/phil/about/philosophy.aspxwhat

For some interesting discussion of these definitions see http://leiterreports.typepad.com/blog/2008/02/what-is-philoso.html

Another definition that has always meant a lot to me is by Wilfred Sellars, an early influence of mine and the philosopher on whom I wrote my undergraduate thesis.

As one of the comments in the Leiter blog entry referenced above discusses, Sellars wrote:

"The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term. Under 'things in the broadest possible sense' I include such radically different items as not only 'cabbages and kings', but numbers and duties, possibilities and finger snaps, aesthetic experience and death. To achieve success in philosophy would be, to use a contemporary turn of phrase, to 'know one's way around' with respect to all these things, not in that unreflective way in which the centipede of the story knew its way around before it faced the question, 'how do I walk?', but in that reflective way which means that no intellectual holds are barred."

I like, especially, Sellars' emphasis on the unrestricted range of philosophical thought ("understanding how things in the broadest possible sense of the term hang together hang together in the broadest possible sense of the term") and the unbounded reach of philosophical methods ("no intellectual holds are barred") -- much of what attracts me to philosophy as an intellectual endeavor is that it licenses unrestricted freedom of thought applied to the "broadest possible" content.