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Toughness determines the amount of shots, which the attackers can withstand with minimal org losses. Basically all enemy attack points are used as single shots and fired on one random target. Each of these shots will reduce your unit's defensiveness (on defence) or toughness (on offence) temporarily by one, while rolling a dice determining whether your unit is being damaged or not. If your unit is out of defensiveness / toughness, the dice roll gets very unfavourable for you.
There's something more to it but that should be the basics.