Branch attack is Valkyrja special attack beside basic attack, they can only be activate using a fixed set of command. Only Kiana, Mei and Sakura can perform branch attack. Bronya, Himeko and Theresa on the other hand uses Charge attacks.
2. Pros and Con
Branch attack deal large amount of damage while can inflict additional status ailments to enemy. In some Valkyrja cases, the Valkyrja uses elemental damage instead of physical, making it easier to bypass some enemy.
Branch attack also receive benefits from some stigmata.
Branch attack require a fixed set of command, they are harder to activate and can easily be interrupted. Having longer animation means you have to cancel out of it before it can deal full damage, some branch attack can leave you full exposed into unwanted situations.