A regular visitor to my philosophy cafe asked me this question after a session, saying knowing this will help him formulate questions to offer at future philosophy cafe sessions. Coincidentally, I had also thought about this very question during my Introduction to Philosophy course last year. Here is the answer I came up with.
A question is philosophical if it satisfies three conditions:
1. The question has not yet been answered by science.
2. There is more than one possible answer.
3. The question cannot be answered by conducting an experiment.
However, it does not follow from this that every philosophical question will be philosophically addressed. A very common practice is to immediately jump to an answer, and to tightly hold on to it against all objections. To philosophically address a question, one must:
1. Assume that the question can be answered.
2. Examine only the argument offered to support any proposed answer.
3. Separate the argument from the arguer.
I hope this will help all future participants of my philosophy cafe -- as well as everyone attempting clear thought.