The Blog of the American Philosophical Association has posted a set of answers to the question "What is philosophy?" collected by David Maclean. Philosopher Simon Blackburn, the author of Mirror, Mirror, provides a particularly memorable answer.
What is philosophy?
“A small pride in standing alongside Socrates dissatisfied rather than the pig satisfied. An endless attempt to find how things, in the widest sense, hang together, in the widest sense. A perpetual openness to new considerations, arguments, insights and perspectives on the problems that beset us, simply because we are conscious, and self-conscious, and therefore want to understand both our lives and the world around us. A desire to profit from what thinkers whose ideas have stood the test of time have left us. A feeling of being especially alive in the hurly-burly of challenge and debate. The pleasure of igniting the interest of students, and of seeing the dawn of understanding in them, as some revelation opens up.
Sometimes the annoyance of finding that I once did not put something as I now think it should have been put. Sometimes as well a battle against ideas that do not stand up as well as their possessors suppose, or even fury at blatant illogicality and unreason. Contempt for those whose scorn for philosophy springs only from ignorance, apathy, or even fear of what it might tell them about themselves. Concern for those whose capacity to think well and act well is impaired by credulity and ineptitude. Fear of power without virtue."
More answers here.