Defining and explaining philosophy is no easy task - the very nature of the subject seems to defy description. The problem is that philosophy, in one way or another, ends up touching upon nearly every aspect of human life. Philosophy has something to say when it comes to science, art, religion, politics, medicine, and a host of other topics. This is also why a basic grounding in philosophy can be so important for irreligious atheists. The more you know about philosophy, and even just the basics of philosophy, the more likely you'll be able to reason clearly, consistently, and with more reliable conclusions.
First, any time atheists get involved in debating religion or theism with believers, they end up either touching upon or getting deeply involved with several different branches of philosophy - metaphysics, philosophy of religion, philosophy of science, philosophy of history, logic, ethics, etc. This is inevitable and anyone who knows more about these subjects, even if it's just the basics, will do a better job at making a case for their position, at understanding what others are saying, and at arriving at a fair, reasonable conclusion.
Second, even if a person never gets involved in any debates, they still need to arrive at some conception about their life, what life means to them, what they should do, how they should behave, etc. Religion typically presents all of this in a neat package that people can just open up and start using; irreligious atheists, however, generally need to work a lot of these things out for themselves. You can't do that if you can't reason clearly and consistently. This involves not just the various branches of philosophy, but also various philosophical schools or systems where gods are unnecessary: Existentialism, Nihilism, Humanism, etc.
Most people and most irreligious atheists manage to get by without any specific or formal study of anything in philosophy, so obviously it isn't absolutely and unquestionably necessary. At least some understanding of philosophy should make it all easier, however, and will definitely open up more options, more possibilities, and thus perhaps make things better in the long run. You don't need to be a philosophy student, but you should familiarize yourself with the basics - and there's nothing more basic than understanding what "philosophy" is in the first place.
Philosophy comes from the Greek for "love of wisdom," giving us two important starting points: love (or passion) and wisdom (knowledge, understanding). Philosophy sometimes seems to be pursued without passion as if it were a technical subject like engineering or mathematics. Although there is a role for dispassionate research, philosophy must derive from some passion for the ultimate goal: a reliable, accurate understanding ourselves and our world. This is also what atheists should seek.
Why is Philosophy Important?
Why should anyone, including atheists, care about philosophy? Many think of philosophy as an idle, academic pursuit, never amounting to anything of practical value. If you look at the works of ancient Greek philosophers, they were asking the same questions which philosophers ask today. Doesn't this mean that philosophy never gets anywhere and never accomplishes anything? Aren't atheists wasting their time by studying philosophy and philosophical reasoning?
Studying and Doing Philosophy
The study of philosophy is usually approached in one of two different ways: the systematic or topical method and the historical or biographical method. Both have their strengths and weaknesses and it is often beneficial to avoid focusing on one to the exclusions of the other, at least whenever possible. For irreligious atheists, though, the focus should probably be more on the topical than on the biographical method because that will provide clear overviews of relevant issues.