You might be asked to write a philosophy of education in a teacher education program, or when applying for a job. Be very careful! This philosophy statement is a window into both your soul and your development. Your potential employers will be able to tell whether you are really ready for the classroom. Be honest, but avoid sweeping generalizations OR specifics. Either will make you sound naive.
A philosophy of education differs for every person. While there may be some similarities, many times teachers teach in very different ways. I have come to believe that the very best teachers are the ones in which their philosophy of education and their philosophy of being are very similar. How one is as a teacher and a person should be very similar given if you fail to be "real" a student will know and will then lose respect for you as a teacher, and person.
To put it in simpler terms than Post #2 does:
Your philosophy of education is your ideas about how to teach. You have to know how you will get the ideas across (will you lecture more or do more "discovery learning"). You have to know how you will try to interact with the students (will you try to be strict or are you more informal).
These are the main aspects of a philosophy of education -- it is your attitude about how to teach and how to relate to students.
This is a fairly large concept. When engaging in defining philosophy, I think that much of it comes back to the basic idea of pedagogy, which refers to the philosophical approach to the manner of instruction and how one teaches. Part of pedagogical approaches is a reflection of what core values one seeks to emphasize in the classroom setting. When engaging in the philosophy of education, there has to be a definition of how the teacher sees themselves in the classroom, how students are perceived in such a setting, and what precepts help to define the process of teaching and learning in the classroom. The philosophy of education is extremely important to the teacher and to the students because it is the foundation upon which all instruction will occur. Without a clear philosophy that guides how individuals in the classroom function, there is a greater likelihood of misfocus and miscalibration in the purpose of instruction within the classroom.
The first answer nails it in my opinion. What I will add is that I find often different in philosophies have to be respected. Some students will do better with teachers of different philosophies. For example a Behaviorist uses very traditional methods. Rote learning is valued. A Progressivist uses more hands-on, inquiry based methods. It has lots more movement, interactive, etc. These are just a a couple.