ToME Wiki
General Info
Combat gives you abilities in melee and ranged attacks. It also allows you a greater weight of equipment without becoming burdened. Combat also affects your pseudo-ID of weapons, armor, ammo and trap kits. If you're an archer it affects how far a piercing shot can pass through. Finally, combat affects which quest you get in Bree after the thieves quest.
Code-Related Information
As I, MrConceit, got most of this from Killerbunnies, I will use his notations. Skill in Combat is denoted as S.
The plus to damage is +S/5 for melee and ranged attacks.
Total weight in pounds of armor for body armor, helm, gloves, boots, shield and cloak you can wear without being burdened is S+20.
Pseudo-ID of weapons, armor, ammo, trap kits, and Demonology eq in your inventory or equipment will pseudo-ID with a probablity of 1/9000(S*S+40) every turn. If S is equal to or greater than 11, the pseudo-ID will distinguish good from great.
A piercing shot will pass through at most S/10-1 monsters. Thus you have to have at least 20 skill in combat to pass through any monsters.
The quest after Thieves quest in Bree will be the Troll quest with the probability of 95 percent if your Combat skill is higher than your Magic skill. 50/50 if they are equal.