There are many meanings now, derived from Greek, French, and English sources.
Explanation:
There doesn't seem to be a single meaning, instead developing over time.
Originally, the prefix "para"- came from Greek and means "next to" and "side by side" and gives rise to words like parallel and paragraph.
Also from the Greek is a sense of "moving or going beyond" and that leads to words like paradox.
It evolved into meaning something that is related to a base word, which gives us words such as paralegal and paramilitary.
Within all this, there is also, form French, a meaning of "para-" that refers to protection or guarding oneself, which leads to words like parachute.
And lastly, the word "parachute: has been shorted and so a word that involves parachutes can have the "para-" prefix, such as parasailing.