Training attack improves your ability to hit in melee combat, and with a few other attacks, such as harm spells. This is a core skill for any melee based character and should be trained to an effective level of at least 100 as soon as is reasonably possible.
The ingame help reads:
Skill duration: random. Type of skill : neutral skill. Affecting stats: St/De/In. It uses no endurance points. The most common form of fighting is hand to hand fighting. Whether this involves a fist, claw or a wielded weapon, it still is necessary to successfully make contact with the target for the attack to work. And as common sense dictates, most targets won't stand still for you to beat upon them. In order to be able to land attacks upon your opponent, you must be skilled in fighting. This requires physical strength, and deftness. A keen mind able to anticipate the opponent is also a desirable trait. Without this skill in fighting, all you will be doing is making holes in the air, which not only makes you look bad, it can make you end up feeling bad as well.