INITIATIVE: The least understood skill. Assur believes Initiative is crucial for actually getting your warrior to attack. Once you are attacking, initiative helps you keep attacking (not letting your opponent get a chance). Low initiative warriors will often just let opponents attack for no reason (and might not try to make an attack when they otherwise would). Realize that it is not your initiative skills alone that determine if you'll attack or keep attacking, but this is what Assur believes initatiative does.
RIPOSTE: After your warrior successfully parries or dodges a blow, your riposte skills come into play. A riposte happens immediately after a dodge or parry, reading something like:
"WARRIOR sidesteps, trying to throw his opponent off balance"
After the riposte message, your warrior may or may not attack (Assur believes after the riposte is where Initiative comes into play), but the message itself is the 'riposte'. Eventually, virtually every successful dodge/parry results in a riposte (Primus & later in the advanced arenas). In basic it is much more important.
ATTACK: How good your warrior is at attacking. High attack lets your warriors "crit" more often. Crits are fancier attack messages and result in higher damage and more hits.
PARRY: How good your warrior is at parrying an attack. Parries can be bypassed, so they aren't as good as dodging, but early on in the game (pretty much through basic), parry based warriors are very, very good.
DEFENSE: How good your warrior is at dodging an attack. Dodge is the most important skill in the very end game. Dodges cannot be bypassed. Even before Advanced Duel2, dodging warrior can make opponents look foolish.
DECISIVENESS: Mostly the ability to strike first in a fight. There may be some other places decisiveness is used, but it eventually becomes one of the least important skills. In basic, though, it is one of the most important skills, especially for pure offensives. However it is also a very fickle mistress, as it is possible for a warrior with a much lower decise rating to attack first. (A large component of who attacks first is determined by die rolls)
-- Assur