A synagogue is a Jewish house of prayer. The term refers to both the building and the institution. You'll also hear the Yiddish word shul, which is actually derived from "school" but has come to mean "synagogue".
Some liberal Jews also use the word "temple" to refer to a synagogue. Usually it's used as a semi-proper noun, e.g. "are you going to temple tonight?". I don't hear "the temple" much in this context. Some (a minority, I think) do it for theological reasons, holding that the Temple has been replaced by synagogues; others do it because that's what they've heard. As somebody who belongs to a "Temple (something)" who doesn't use the word "temple" in this way, I notice this a lot.
The Temple (usually written with a capital 'T', for both clarity and respect) is the temple in Jerusalem that was destroyed by the Babylonians in 586 BCE, rebuilt, and destroyed by the Romans in 70 CE. Jews pray for the rebuilding of this temple with the coming of moshiach (the messiah).
A congregation is a religious community. Often it has an associated synagogue, but congregations can also gather in other places -- people's homes, schools, etc. The generation that spent 40 years in the wilderness was a congregation (the torah uses the word kehal to refer to them at times).
People sometimes use the word "congregation" to refer to the synagogue, too.