1Calm and unshaken no matter what happens; can also mean not caring about or being indifferent to something.
どんなに怒られても彼は平気な顔をしている。
No matter how much he gets scolded, he keeps a calm face.
高いところが平気な人もいれば、怖くて足がすくむ人もいる。
Some people are perfectly fine with heights, while others freeze up in fear.
彼女は失敗しても平気で次に進む。
Even when she fails, she calmly moves on to the next thing.
虫が苦手な人が多いが、彼は平気で素手で触る。
Many people dislike bugs, but he touches them bare-handed without any concern.
2A casual way of saying "I'm fine" or "no problem."
「一人で平気？」「うん、平気だよ。」
"Are you okay by yourself?" "Yeah, I'm fine."
少しくらい遅れても平気、気にしないで。
It's fine even if you're a little late, don't worry about it.
「熱いけど食べられる？」「平気、平気。」
"It's hot, can you eat it?" "I'm fine, I'm fine."