To be philosophical is to stay detached and thoughtful in the face of a setback, or to approach a tough situation in a level-headed way. When his girlfriend left him, Bernard was philosophical: "If she loves me, she'll return."
In ancient Greece, philosophy literally meant a love of knowledge and wisdom. In modern times, the field of philosophy is more specifically the study of how we think through problems. Great philosophers have all sorts of theories about how and why we think and act the way we do, but the word philosophical often just means that you choose to be more thoughtful and look at the 'big picture' when dealing with challenges.