Conviction (capital C) in Exalted is a stat, one of the four Virtues upon which Creation is metaphysically based (there is a fifth, Willpower, but it is more of a meta-Virtue and closer to what we mean colloquially by conviction in our world).
In any effect, Conviction is a stat that can be applied to aid you in the following situations, and only the following situations: “Withstanding hardship and torture. Making decisions when all options are horrific. Committing atrocities to accomplish a goal.”
Conviction is the Hard Man Making Hard Decisions stat. You don’t have to be puppy-kicking to have it high, but unless you are using it to withstand or inflict horrible things, it doesn’t help you at all.
The other Virtues are Compassion (“Protecting or aiding the sick, innocent or oppressed. Fighting for justice. Bringing aid to the needy. Fighting for or engaging in romantic love.”), Temperance (“Resisting temptation. Holding your temper when taunted or struck. Holding your tongue while intoxicated. Overcoming the effects of illusions, drugs, poisons and mind control.”) and Valor (“Heroism in battle. Withstanding magically created terror. Performing feats of daring and taking risks.”)