Traits are always present, they are like a permanent buff. They have no cooldown, cannot be removed or disabled, and do not need energy to work. That's the reason why they are also known as passive abilities, or just Passives.
Runes have a Passive as 4th stat. That Passive is added to the hero when the rune is fully leveled up and inserted into a rune slot of that hero.
Sometimes a trait is inactive until you team up that hero with another hero. Often it's a Legendary hero that activates slumbering traits. For example: If you team up Torchy with Solaris then Torchy's Beastly Recklessness will be active and the little bat will spread fire all over the dungeon.
You can inspect traits and abilities on the hero profile when you tap and hold the icon. On the "Ascend" tab you will find traits that are unlocked on the next Ascension. They are displayed together with Abilities.
In the dungeon you can tap and hold any hero or enemy to inspect their traits, abilities, buffs and debuffs. Unfortunately there is no hint for the type of the icon. If you're unsure what type the icon is then have a look at the health bar of the character. Buffs and debuffs are displayed on top of the health bar.
The Way a Trait Works
Traits might be inconspicuous but have a deep impact on the team and the battle.
A trait can trigger revenge attacks, or an additional attack, or it increases fire power by boosting stats or boost the damage.
There are traits that protect allies, allow a hero to revive an ally, to heal allies passively. Serval traits grant immunities, resistances, or damage reduction. A few even remove corpses, or spawn skeletons.
How a Trait Affects the Team
Traits can boost single stat like attack (ATK) or health of allies. The ally must match a certain criteria like: must be Fire Hero. If the hero with the trait also matches the criteria then they get the boost, too. For example Bovus El Doro's Warrior Heart boosts his own health and the health of his Warrior allies by 25%.
Other Traits can provide additional energy for the team to have Abilities ready at the beginning of a battle, like Kobal the Pestilent's Dark Deception does. Or during the battle like Indigo with her Critical Energy does.
And other Traits again allow the hero and their allies to deal boosted damage by adding some percent to the damage or even multiply the damage. The boost can be individually like Challenge Accepted or affect certain allies to like Agnon's Dark Skies does (Flying allies deal 2x boosted damage to non-flying enemies).
Tips & Tricks
Most things in the game display a tooltip when you tap and hold them. On the tooltip for abilities you can see also their cooldown times. During a battle there are active debuffs and modifications like Snow Day added to the tooltip.
In the dungeon you can tap and hold any hero or enemy to inspect their traits, abilities, buffs and debuffs.