The Vallorian Valor will produce vallorian guards for you. You don't unlock those units until Chapter 10 and they are then trained in the Mercenary Camp, so you'll get a few with this event building way before you can make them yourself.
I think the quest you're probably seeing is unrelated to your winning this building. In Chapter 3 you unlock the Training Grounds and I'm guessing your quest is to build the Training Grounds. If you've unlocked the tech for it in the research tree, it will be in Buildings under the Military tab.
You'll eventually have 3 military training buildings: Barracks, Training Grounds (unlocked in Ch 3), Mercenary Camp (unlocked in Ch 7). These building allow you to train different units. Upgrading them increases the speed at which they produce the units. Armories determine how many units they produce at one time (training size). The more armories/higher armory levels the more troops trained at once. There are also Ancient Wonders that improve training time on the training buildings as well as wonders that increase the training size. The trick is to balance these things so your training queue will run 24/7, not 'running out' when you are AFK for work or sleep. In my baby city (Ch 4), I'm almost balanced, losing 1-2 training hours/day due to it running out when I'm AFK.