Ease means to lessen or release, often making something possible in the meantime. When you put someone at their ease, you lessen their discomfort. When you ease into a chair, you gently release yourself into it.
A life of ease means you do not have to struggle to make money. Your dad might be mad if you pierce your nose, but eventually, with time, his anger will ease and he will ease up on you. Your older siblings' behavior will ease the way for you to do things that frighten your parents without their overreacting.