I am sorry to say that although I have a BA in Phil from a highly reputable research university, I do not know exactly what it means either. Maybe it means holding up a Phil text to a mirror and seeing its reflection!
The best I can make of it is as follows. Insofar as reflection involves the spirit of something bouncing off something else, I take it that philosophical involves a superficial examination of something from a philosophical perspective. Say something happens to you during the day. You go home and review what happened in accordance with philosophical methods, or in accordance with objects of philosophical inquiry.
Philosophical methods largely involve the use of logic, and the use of concepts like necessary and sufficient conditionality, and disambiguation of terms. Objects of phil. inquiry include the natures of reality, knowledge, right action, modality, logic, science method, mind, language.
If you bounce an idea or the details of an event off the methods or objects of philosophy, then I guess you are philosophically reflecting.
Is it important? It must be. People have been doing it for a long time, to some extent or other, and however astutely. Better yet, now that I have laid out a reasonable answer to the first part of your question, can you determine for yourself whether it is important to you?