This skill unlocks an attack "Quell the beast", which allows you to tame an animal. As of the latest update, this skill also unlocks an action, "Propose", which allows you to initiate an engagement maneuver. Your STR and CON must be at least two times as high as the animal in question. Tamed animals require food or grassland to survive and breed. See Taming for a detailed guide on how to tame an animal.
Animals that can be tamed:
How to UseEdit
To gather wool from sheep you equip a sharp item (such as a stone axe) and right click -> sheer on the sheep. If the option does not appear when you right click then said sheep has already been sheered. It is unknown how long it takes for a sheep's wool to regrow.
Animal Husbandry is the skill that allows your character to milk cows and shear sheep.