What does the word でしょう mean?
My Japanese teacher is always saying the word でしょう but he's never told us what it means. Can someone tell me what it means and how to use it in a sentence please.

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The closest equivalent in english would probably be "isn't it?" or "isn't that right?". Its only a semi-question though and is mostly used for inviting someone to agree with you. It can be used in place of です t the end of a sentence. Just replace The す with しょう ^^

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As Rayne said, it comes from です and the meanings of it depend on the intonation and on the context.

The main use of でしょう are:
To express about the future, guess, uncertain things. 
あした、かれはパーティにくるでしょう。(Tomorrow, he'll come to the party / I think he'll come to the party.)

When we recommend something to someone or express our thought with humble feeling
It would be better use this word. (この単語を使うほうがいいでしょう。)

With the intonation ⤴︎, it's like "....., isn't it / aren't you / don't you?" in English (with expectation of having the same feeling). 
My puppy is cute, isn't he? (私の犬はかわいいでしょう？)

I hope this was helpful.

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でしょう／でしょ is an expression that expresses uncertainty or doubts. There are also different ways to use でしょう。

Example:
あしたは　あめが　ふる　でしょう - It probably will rain tomorrow
つかれた　でしょう。 - Tired, huh?

If you have more questions, just ask :3