na-adjective
Describes a state of inner calm, free from worry or agitation. Often used when one's mind is settled after anxiety or in a peaceful situation.
温泉に入って、心穏やかな気持ちになった。
Soaking in the hot spring, I felt my heart become calm.
彼はいつも心穏やかで、怒ったところを見たことがない。
He is always serene; I've never seen him angry.
穏やか can describe weather, personality, or situations as mild/gentle, while 心穏やか specifically refers to one's inner emotional state.
落ち着く is a verb meaning 'to calm down' or 'to settle', often used for regaining composure, whereas 心穏やか is an adjectival noun describing a sustained peaceful state of mind.
Compound of 心 (こころ, 'heart, mind') and 穏やか (おだやか, 'calm, gentle'). The exact historical derivation is uncertain, but the combination transparently means 'calm-hearted'.