How does resistance work?
[...] Roll the die, and add the number rolled to the target’s AC against that attack. If the attack still hits, the target has resistance against the attack’s damage. [...]
What is the resistance? Is it a value you subtract from the damage, and if so what is that value?
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Resistance is a game term which means that a creature takes half damage from a specific source.
From the Player's Handbook (pg. 197)
If a creature or an object has resistance to a damage type, damage of that type is halved against it. If a creature or an object has vulnerability to a damage type, damage of that type is doubled against it.
Resistance can come from many sources, including racial traits, class features, monster special traits, and spells. For example, Tieflings have a racial trait that gives them resistance to fire damage.
Also note that you always round damage down, so 15 damage becomes 7, not 8.
There’s one more general rule you need to know at the outset. Whenever you divide a number in the game, round down if you end up with a fraction, even if the fraction is one-half or greater. (Basic Rules, p. 4)
In this case, if the attack hits the target (even after adding the AC from Warding Maneuver) you divide the damage the target would take by 2.
If a character has resistance to something, for example, piercing damage, that damage type is halved against it.