Resistance is the measure of the health of a templar's immune system, how well his/her body handles routine anti-radiation medicines, as well as the small tweaks he/she has made to his/her armor to redirect external heat sources away from less insulated joints and vents.
Resistance acts similar to bonus Armor but unlike armor, cannot be penetrated and only applies to non-standard damage such as Fire and Radiation. Resistance is granted by a class multiplier and a templar's willpower. So a templar with a class multiplier of 150% and a willpower of 6 would have 6 * 1.5 = 9 resistance. Fractions are rounded downward, so a willpower of 7 would only result in 10 resistance in this example.
Resistance is subtly different than the element-specific Res and despite one seeming to be an abbreviation of the other, they are independent statistics.
Suppose an attack of 40 standard damage and 30 radiation damage lands on your templar who possesses 10 Resistance. Further suppose that the blow was not penetrating and you have 44 armor and you roll a maximum armor roll, utilizing all of that armor perfectly. Great! You take no standard damage. However, you still have to deal with the radiation component. Your armor is useless here, even though you had a surplus of 4 armor points. We will further assume you have no radiation-specific Res. Similar to Toughness, half of your Resistance will be applied against the radiation damage, and the other half will be rolled as a single "big die". The result from that roll will also be reduced from the total damage your poor templar will suffer.
end damage = damage - 0.5 * resistance - random(1, 0.5 * resistance) = 30 - 0.5 * 10 - random(1, 0.5 * 10) = 30 - 5 - random(1, 5) = 25 - random(1, 5) = uniform distribution from 20 to 24 damage.
Resistance is a way to soften up the less common forms of damage that will totally ignore your armor. It will also protect you from environmental fire damage from burning tiles you pass through and the heat cost you have applied to your templar from moving through those tiles.