There are many meanings now, derived from Greek, French, and English sources.
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, from 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 shortened and so words that involve parachutes can have the “para-” prefix, such as parasailing.