だろう is a conjugated form of
だ, and can also be seen in the contracted form
だろ (more casual).
だろう expresses that the speaker thinks that something is true (assertion/expectation), and also that the listener would probably agree with them. This comes across like ‘right?’, or ‘probably’ in English.
-
お前（まえ）、明日（あした）パーティーに行（い）くだろ？
You are going to the party tomorrow, right?
-
明日（あした）は晴（は）れるだろう。
It will probably be clear tomorrow.
だろう carries exactly the same meaning as
でしょう (the polite equivalent). However, due to だ being more casual than
です,
だろう is also considered to be more casual/masculine than
でしょう.
While
だろう is usually used when the speaker has some sort of information that would support their assertion, it can also be used simply when the speaker ‘feels’ that something is true.
-
これは、お菓子（かし）だろう？
This is candy, isn't it?
In this kind of sentence that expresses a ‘feeling’ or ‘hunch’,
だろう comes across as quite low confidence. The speaker's tone of voice will often reveal how confident
だろう is.