Freemasonry is a
fraternal organization with a
ritual tradition. It uses the terminology of actual, working
masons (that it, people who work with
stone for a living) in an elaborate correspondence with various philosophical ideals such as
honesty or
fairness. It is not a
religion, but does require belief in some form of
deity; no
atheist is permitted to join.
My understanding of its probable history is that Freemasonry is a few centuries old, and that within the context of rituals, a claim is made for continuity to before 1000BCE. This does not mean that Jesus' contemporaries included Masons (although surely there were working masons), but merely that they draw from historical and biblical imagery.
I am not a Mason, so take this with a grain of salt. The main reason Masons don't bring up Freemasonry in conversation is not that their membership is secret (it isn't). The main reason, according to a Mason friend, is that they don't want anyone to join unless they truly want to, and so to avoid creating peer pressure, Masons refrain from anything like proselytizing. As a result, some Masons are quite glad to discuss everything but ritual secrets -- but you have to bring up the topic. This idea is sometimes seen on bumper stickers as "To be one, ask one" (or 2B1 ASK1).