Someone who's living is alive. You might talk about your living grandparents to distinguish them from the ones who died before you were born.
When you talk about animals and people, you can call them living beings. and you can also use this adjective to mean "used" or "active," like a living language that continues to be spoken. As a noun, living means the state of being alive or "enough money to live." You might say, for example, that you write poetry for fun, but you work cleaning hotel rooms to earn a living.