The Septuagint is an ancient Greek translation of the Hebrew scriptures (The Old Testament). It is often referred to, in shorthand, as the LXX. The name means "Seventy" (hence LXX). It is named after the 70 scholars who wrote it.
After Israel was hellenized, it became popular, in Israel, as the everyday-man's scripture since Greek was spoken more often than Hebrew. It is commonly referenced in Christian circles because it is the translation that was used by Jesus and the writers of the New Testament when they were quoting the Old Testament. That is one of the reasons why the New Testament quotes of Old Testament scripture don't line up, word-for-word, with what you find in the Old Testament. It was a somewhat loose translation of the Hebrew, roughly akin to the looseness of the modern NIV.
It has been immensely useful to those studying ancient Hebrew because it is a sort-of Rosetta Stone, providing slightly-more-modern Greek translations of ancient Hebrew words. It is also important because, even though it is only a translation, it is older than many of the Hebrew manuscripts for the books in the Old Testament.
No one knows specifically who the 70 scholars were who wrote the Septuagint, but the traditional story is that Ptolemy II, a King in Egypt from 283-246 B.C., commissioned it so that it could be used by the Greek-speaking Jews who were living Egypt at the time.