A Power trait governs the four unit attributes that are understood as physical power in real life: Strength, utilization of strength (Attack Skill), agility (Defence Skill), and speed (Combat Speed). There are many of these, but only seven are used in-game:
Power of the Turning Year, tied to Turn Count
Dark Power, tied to Darkness
Storm Power, tied to
Storms
Scalar traits provide a stat bonus equal to their listed value multiplied by the level of a certain scale in the unit's province. For example, the unit with Cold Power (2) in a province with
2 scales would gain +4 to the relevant stats. However, if local scales are in the opposite direction, these traits provide a stat malus instead. The same unit in a
2 province would have -4 to its stats. This means they can be very swingy, having a huge effect on the unit's combat effectiveness depending on the local scales.
The scalar traits include Fire Power, Cold Power, Chaos Power, and Magic Power.
Chaos Power is special: it also counts Unrest. For every 30 points of local Unrest, add 1 to the Turmoil value of the local province, but only for the sake of this trait. This extra unrest power is capped at +3 at 90+ unrest. In any case, Turmoil bonus caps at 5, even if unrest bonus + turmoil would be higher.
Magic Power also affects Magic Resistance, negating the positive and negative effects of Magic/Drain scales on the stat. It also affects Stealth; only, instead of +1 per positive point, it gives +10.
Philosopher is not a Power Trait; it works in the exact same way, but it only affects Research Skill. It scales positively with Sloth, and negatively with Productivity.
These traits provide their listed bonus under certain conditions. They do not provide a stat malus in the opposite conditions, however.
Dark Power is activated when the battlefield is cast into darkness, which occurs in the following scenarios:
Units with Dark Power also often have Darkvision, which further exacerbates the stat difference between them and other units that cannot see in the dark.
Storm Power only cares if a Storm or a Blizzard is in the current battle. If there's none, there's zero Storm Power; otherwise, the bonus is 1. Whatever it is, multiply this by the value of the trait.
Storm Power typically comes with Storm Immunity. For those without Storm Immunity, Storms halve Precision and prevent Flying. Storms also cause half of nonmagical missiles to end up nowhere, which may or may not affect the Storm-Immune.
Power of the Turning Year provides its listed bonus on every third turn after turn 1, or any turn where the season is listed as just its name instead of "Early " or "Late "; in the user interface, these turns are merely referred to as Spring, Summer, Autumn, and Winter.
Power of the Turning Year does not affect Combat Speed, for some reason.
There's also a similar series of traits, "Strength of the Season", which take effect in certain seasons; these do not interact with any of the Power attributes, however, but rather Hit Points.