The Socratic question is the question about who exactly Socrates was in real life. He did not write anything down himself. All we know about him comes from the writings of others. Some of these sources are very dubious. Plato wrote the most complete record of Socrates's life, but we have no way of knowing how far he stretched the truth. One thing is known for sure; Socrates was not a pretty man. In spite of this fact, he was quite popular with young men.
The Socratic method is a method of questioning. Socrates does not
lecture or give speeches. Rather, he asks questions of his pupils. He asks
very pointed and critical questions, sometimes even leading his interlocutor
into a philosophical trap! Today we use this term to refer to any kind of
questioning that a teacher does in order to encourage a student to give the
answers to questions on his or her own. Sometimes it still means leading
students into a trap by asking leading questions. Don't worry, I won't try to
trap you! But it's not a bad rule in general to be wary of leading questions
when you're dealing with philosophers.