Very briefly, philosophy might be regarded as a conceptual enquiry dealing with fundamental issues relating to life, knowledge and values. By conceptual enquiry we mean an enquiry that relies primarily on critical reasoning. This includes :
In such respects philosophy is more like mathematics and logic. However, the subject matter of philosophy is more general in that it deals with all sorts of different areas outside mathematics and logic, such as religion and morality.
Although philosophy is different from science, it would be a mistake to conclude that philosophy cannot contribute to the development of science. Philosophers can help scientists clarify the basic concepts in scientific theories, and use their skills in logic to evaluate the strength of evidence supporting or criticizing particular theories. Many sciences (e.g. psychology) originally developed out of philosophy.
There are other reasons for doing philosophy apart from pleasure. First, philosophical skills in thinking and writing and help us in describing and understanding theories and ideologies. Here philosophers take up the task of a cartographer, mapping out conceptual terrain and logical structure.
Second, as mentioned earlier, philosophy can be an important tool in helping us acquire knowledge. Logic and critical reasoning are necessary to achieve consistency and in determining the right conclusions to be drawn given our observations and experiences.
Finally, philosophy can also play a transformative role in our lives and social institutions. Through critical reflection on the justification and coherence of the values in social practices and our own actions, we do not just acquire a deeper understanding of our culture and of who we are. This understanding can also pave the way for us to improve ourselves and the world around us.
It is perhaps more useful to distinguish between history-based and problem-based approaches. A history-based approach to philosophy aims at understanding the history of ideas, the evolution of intellectual currents at different times, and what particular thinkers thought about certain philosophical problems. A problem-based approach is more concerned with understanding and solving particular philosophical problems, such as whether God exists. It pays more attention to the validity of the relevant arguments and care a bit less as to whether the arguments capture exactly the thoughts of past thinkers.