The only Metron seen appeared to be a young, lightly-built humanoid with gray skin. Whether this appearance is actually typical of their race is unknown. Despite his youthful appearance, the Metron representative claimed to be 1500 Earth years old.
The Metrons can either teleport themselves or project images of themselves without any obvious technological apparatus. They were able to easily immobilize a Constitution-class starship and the Gorn ship without revealing their own location. They teleported Captain Kirk and the captain of the Gorn ship to a planet an unknown distance away for their duel.
Nothing is known about how the Metrons govern themselves. They resent intrusions into their territory, especially if the intruders are engaged in hostilities. The extent of their territory is unknown.
The Metrons consider mercy to be an "advanced trait", meriting a change in their attitude towards humanity when Kirk chose not to kill the helpless Gorn captain.
The Metrons appear to possess immense power, whether it is inherent or technological. They could presumably overcome any of the major powers in the Alpha Quadrant if they chose to do so, but they have no apparent interest in conquest. They should be considered extremely dangerous to any would-be invader, however.