The Prophets do not have a material form. Within the wormhole they inhabit, they appear as swirling blue clouds; outside, they must inhabit the body of a third party to interact with their environment. While inhabiting physical bodies, they are capable of firing destructive energy blasts. No matter their form, the Prophets are extremely vulnerable to chronitons.
The Prophets claim to have no concept of linear time. While this claim would seem dubious at best, they have been known to unwittingly create ontological paradoxes such as the conception of their Emissary.
When communicating with visitors within the wormhole, the Prophets use elaborate visions based on critical events in their guest's past. While these visions feature many speaking "characters" taking the role of the Prophets, it is unknown if they in fact depict different Prophets, or if they are all controlled by a single entity.
For thousands of years, the Prophets have interacted with the people of Bajor through various emissaries and artefacts. The purpose of this interaction is something of a mystery; at times the Prophets show little regard for the Bajorans' well-being, while at others they go through great lengths to safeguard them.
Prophets that have been banished from the Celestial Temple are known as Pah-wraith. The reason for their banishment is never explicitly stated; statements by their Emissary, Gul Dukat, suggest they plot to dominate the Alpha Quadrant. Some Pah-wraith are imprisoned in the Bajoran Fire Caves, others in various artefacts. Battles between escaped Pah-wraith and Prophets are known as Reckonings.
The Prophets remained neutral during the opening stages of the Dominion War, allowing Dominion ships free passage through the wormhole. They eventually sided with the Federation to protect their Emissary, destroying or displacing a Dominion fleet attempting to reach the Alpha Quadrant.
The Prophets created and distributed ten "Orbs", devices that induce the visions through which the Prophets communicate. One of the Orbs allows for controlled time travel, though the mechanism by which it operates is unknown.
While they have vast power over anything passing through the Bajoran Wormhole, the Prophets have little interest in events occurring outside the wormhole. They have some interest in the well-being of the Bajorans, but they rarely take any significant action on the Bajorans' behalf (possibly because of their odd perception of time). Prophets encountered outside the wormhole have superhuman abilities, but are far less powerful and more vulnerable than inside the wormhole.
The Prophets can be regarded as a minimal threat to any force that does not directly threaten Bajor or pass through the Bajoran Wormhole.