Fighting in Armageddon is handled very differently than in other places. The system is complex and (hopefully) realistic.
First, a combination of the attacker's offense score, weapon skills, position (riding, standing, sitting, etc.), and other factors, are added to a random number. Second, the defender's defense score is combined with their ability to parry, factors affecting their position, and a random number. Then, quite simply, if all of the offensive modifiers are greater than all of the defensive modifiers, the defender is hit.
Once someone is hit, they will be struck on a specific body location, and if they are armored in that location, the damage may be lessened or negated entirely (though stun damage will probably still accrue). Note that some places are more painful to be struck in, such as on the neck (almost all races suffer far more damage when hit on the neck).
Injury can be in terms of health points, stun points, or both. It is possible for your character to be relatively intact, but knocked out.
Bear in mind that fighting while mounted can be extremely risky, since characters are much easier to hit, and generally sustain worse wounds, due to mounts being less maneuverable than a character on foot.
There are no combat rounds. The frequency with which one may attack is based on one's agility score.