Binding Vows are only within casual 1v1's. There are a total of 5 Binding Vows, but you are given 3 to choose from in every casual 1v1.
Credits to NoobEternally for the pictures (Except for the first one)
Binding Vows:
Your skills cooldown and ultimate bar will be shown next to your character for the opponent to see. But you get 10% more hp
Your dmg will get limited to 90% for the first half of the match. In the other half, your dmg will increase to 110%
One of your skills will get removed. In return, you will get 20% more HP.
The skill removed is randomized every time you die
Every skill will get a 30% dmg increase. However, you can only use a skill once
Increases the ultimate bar to 130%. However, you will die when your ultimate bar is empty