One of the most common ways でしょう is used is to express supposition or a guess about something. It's equivalent to English expressions like probably, maybe, or I guess.
By using でしょう before the question particle か, you can make a question more tentative. In this way, the question sounds softer, less direct, and more polite.
|Could this be your pen?||これ は あなた の ペン でしょう か？kore wa anata no pen deshou ka?|
|Might you be a teacher?||あなた は 先生 でしょう か？anata wa sensei deshou ka?|
Just as the particle ね, でしょう can also be used to seek confirmation. The difference is that when using ね, the speaker is fairly confident that the listener will agree, whereas with でしょう, there is more uncertainty about whether the listener agrees.