Rage is a mechanic that you can't visually see, but it effects your chances to unlock a ssj form. Every time you die to a boss your rage goes up by 1, up to a maximum of 5, rage goes down every time you kill a boss as well. The chance of getting a form is subtracted by your rage. So for Super Saiyan 1 for example, its a 1 in 10 chance, at 5 rage it would be a 1 in 5 chance instead.
The chance to get a form can not go below 1 in 2 chance.