Cicero explained religion in his book "De Natura Deorum" - "The Nature of the Gods" (in book 2, part 72). He wrote that Religion originally meant "relegere", from "re- legos" or "re-logos", meaning to go through the logos (or reasons) for something.
So religion means the study of logic. Or at least it should, unless Bible Goggles turn it into a worship of the supernatural.
Cicero contrasts the religious (those who understand reasons) with the superstitious: from the word "superstes" meaning survivor. The superstitious are those who think they will be blessed (i.e. they or their children will survive the harsh world) simply because they believe the right things or obey the right rules. That describes modern religion, but it is the opposite of Cicero's concept.
Later Christians (such as Augustine) viewed religion through their supernatural goggles, so they changed religion to mean "religare" or "to bind fast", in the sense of "place an obligation on". (See the Online Etymological Dictionary). A system of logic (re-logos) was gradually replaced by a system of blind obedience (religare).