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安心 can be defined as relief, peace of mind, feeling at ease, to be relieved, to set one's mind at rest, and easiness.
安心 is a nice word that encompasses great meanings within just two characters. Some of the other meanings include pacifying, settling the mind, and peace of mind. It's also the idea of feeling a sense of security, safety, and confidence in your state of well-being.
This can be used by everyone, but some consider it to be a Buddhist concept (You'll find it in your Zen dictionary).
Note: Can be romanized as Anshin or Anjin in Japanese.