The previous answer is headed in the right direction, but isn't quite right. Philosophy is a non-person, so "it" doesn't seek to grow in wisdom; it doesn't seek anything at all. Philosophers generally do try to move forward with their knowledge, and are said to be motivated by this "love of wisdom."
Dialectic (not dialects) is a very important part of philosophy, but might be better understood in terms of being a discussion or dialogue about important issues. One cannot have a dialectic alone, and so we need to add the conversational component to the previously stated ideas of "logic and reasoning."
As for philosophy's interaction with education, at least two things can be said:
1) The education of philosophy involves learning the discipline or methods of formal philosophical reasoning, and often the history of philosophy as well.
2) The philosophy of education involves teachers or educators thinking through why they teach, how they teach, why they teach the way they do, and what aspects of their role as educator are prioritized above others. Many teachers have the intrinsic worth of the student as a person in mind when they decide how they will prioritize their duties.
In short, philosophy is an essential component of education in any subject, and you don't have to be a philosopher to have a philosophy.
Here's a link to the eNotes summary page on philosophy!
Philosophy literally means the love of wisdom in Greek. Phil = love; sophos = wisdom. I think when philosophy is at its best, it seeks to do exactly that; it seeks to grow in wisdom, usually through dialects. This simply means that philosophy uses logic and reasoning to find out things like: "how do we know what we know?" Or a question like what makes something moral or immoral. From this perspective, philosophy is something that all people do. As for the importance for education, philosophy enables one to think better and more critically. So, it is recommended.