Overview
The Q are a unique race, and they possess many extraordinary, "God-like" powers including the ability to manipulate time, space, matter, and energy. They have an almost omnipotent ability to perceive and know events in the past, present, and future. They are invulnerable and immortal except when faced with weapons designed by others of their kind: in sufficient numbers, Q can strip other Q of their powers and make them mortal or make them any lifeform they wish.
It is suggested through their appearances on the various series of Star Trek that the Q have evolved since the Big Bang to their current state, and that possibly they were like humans very early on.
One member of the Q once referred to a "New Era" among the Continuum, during which an important change occurred in the species. No further details were given. The Continuum is on a separate plane of existence and thus not subject to linear time as normal space is. It has been suggested by Quinn that when the Q gave up their physicality and achieved their godlike powers, they also gave up any chance of growth or evolution, thus leading to stagnation (since change was unnecessary).
They usually appear as human simply because they can assume any form they wish, and when interacting with humans they usually appear as one of them to make the humans feel more comfortable.
In the episode "All Good Things..." Q mentions that humanity or possibly captain Picard is destined to explore existence itself. Q's meaning of that statement has never been explained in any episode or movie of Star Trek.
Read more about this topic: Q Continuum