I have read many dictionary definitions and there seems to be two possible sources of the word trivial. Online dictionaries say it's from latin tri and via, "three ways" or "crossroad", basically meaning "street talk" or "corner talk", however this Q&A site states it more likely from trivium, which means "first three of the seven liberal arts", and strongly influenced by the former. I am not quite sure how to interpret the etymonline.com explanation.
OED to the rescue again...
So yes, it comes ultimately from trivium = "three ways", but A.5 says
Trivial comes from the Latin trivialis which means very much what trivial does. Quite how the Latin trivialis was derived from trivium is beyond the scope of an English site, but it may well be to do with idle chatter on a street corner.