Toughness is the measure of sheer grit a templar has to survive, the capability to shrug off lesser blows, and sometimes even the protective scar tissue formed beneath the layers of Templar battle suits from repeated exposure to deadly Xeno claw and Hex-shells alike.
Toughness acts similar to bonus Armor but unlike armor, cannot be penetrated. Toughness does not protect against non-standard damage such as Fire or Radiation. Toughness is granted by a class multiplier and a templar's fortitude. So a templar with a class multiplier of 150% and a fortitude of 6 would have 6 * 1.5 = 9 toughness. Fractions are rounded downward, so a fortitude of 7 would only result in 10 toughness in this example.
During an attack if, after armor has been accounted for, a positive number of damage points remains, half of toughness will immediately reduce it, and the remainder of toughness will be rolled as a single die to reduce it further. (Because the minimum roll of a die is always 1, you effectively are always guaranteed (toughness / 2) + 1 reduction.)
So if damage after armor is 20 points, and toughness is 10:
end damage = damage - 0.5 * toughness - random(1, 0.5 * toughness) = 20 - 0.5 * 10 - random(1, 0.5 * 10) = 20 - 5 - random(1, 5) = uniform distribution from 10 to 14 damage.
Toughness can be thought of as a stop-gap measure to help templars with armor that has low deflection but there really is no good substitute for high armor or simply not being in range of attacks.