a polite conjectural form expressing probability or a tentative assertion (polite form of だろう); 'it seems', 'I think', 'probably'.
明日は雨が降るでしょう。
It will probably rain tomorrow.
彼はもう着いているでしょう。
He is likely already there.
この仕事は来週までに終わるでしょうね。
This work should be finished by next week, I think.
a tag-question or seeking agreement ('right?', 'isn't it?'); less formal 'でしょ' is often used in casual speech.
これ、おいしいでしょう？
This is tasty, isn't it?
君も明日来るでしょう？
You're coming tomorrow too, right?
今日は寒いでしょう？コートを着ていきなさい。
It's cold today, isn't it? Wear a coat.