The higher this attribute, the closer you are to beasthood when temporary transformed.
Beasthood is a stat that determines the maximum damage boost you can reach while under the effects of a Beast Blood Pellet or the Beast Claw weapon. The Beasthood score is handled much the same way as a status resistance stat: it gets reverse scaling from your Insight score (like Frenzy), it can be boosted by wearing Attire, and can be further boosted with the Beast Rune. Beasthood buildup can be cleared by using a Sedative, like Frenzy.
As the meter rises, physical damage dealt with your weapons will increase while all defenses decrease. Arcane, Fire, and Bolt damage are not boosted. Effect is determined by how much Beasthood is currently built up in the meter, not when maxing the meter. If you have a Beasthood score of 400 and have built up 25 Beasthood so far, your character will have +30% more physical damage and all defenses reduced by -30%. Completely filling the meter has no special effect, aside from not being able to increase Beasthood any further.
While the effect is active, attacks with your right-hand weapon will add Beasthood to the meter. Generally speaking, R1 attacks add the least amount of Beasthood while R2 attacks, transforming (L1) attacks, and L2 attacks (when available) will add the most. Ludwig's Holy Blade and the Kirkhammer are the exceptions to this as their trick mode R1s build up Beasthood as fast as heavy attacks, and Logarius' Wheel can rapidly increase the meter due to its multi-hit attacks.
Note that the meter is constantly depleting, so it's a good idea to have slightly more than 300 Beasthood if you ever intend to use it. Otherwise, you'd hit 300 only for it to drop back to 299 in the next instant, meaning you'd never get the 300 bonus. Something like 350 is enough when using Beast Blood Pellets as their effect only lasts for one minute, while the Beast Claw can benefit from as much as 500 so the +70% physical damage boost will last between enemy encounters.
1 Beasthood : +20% phys attack, -20% all defenses
25 Beasthood: +30% phys attack, -30% all defenses
50 Beasthood: +40% phys attack, -40% all defenses
100 Beasthood: +50% phys attack, -50% all defenses
200 Beasthood: +60% phys attack, -60% all defenses
300 Beasthood: +70% phys attack, -80% all defenses
All of these changes can be seen under the Stats menu.