A conjectural form of the copula 'だ' used to express supposition, opinion, or expectation (e.g., 'I think..., it seems...').
明日は雨だろうから、傘を持って行った方がいいよ。
It will probably rain tomorrow, so you'd better take an umbrella.
彼はもう着いただろうと思って電話した。
I thought he had probably already arrived, so I called.
そんなに難しくはないだろう。
It probably isn't that difficult.
来週までに終わるだろうか。—終わるだろう。
I wonder if it will be finished by next week. — It should be finished.
A tag or confirmation seeking form (e.g., 'right?', 'isn't it?'), also used to express 'I thought so' or to prompt agreement.
今日は寒いだろう？上着を持って来た？
It's cold today, isn't it? Did you bring a coat?
君もそう思うだろう。
You think so too, don't you?
『彼は来ないよ』『だろうね』
'He won't come.' 'I thought so.'