To be able to exist or stay in a place; expresses the ability or possibility of being somewhere.
ここにいられるなら、毎日来たい。
If I can stay here, I want to come every day.
この部屋には長くいられないので、早く戻るよ。
I can't stay in this room long, so I'll go back soon.
彼は一日中家にいられるタイプだ。
He's the type who can stay at home all day.
(Used in the phrases 〜ずにはいられない / 〜ないではいられない) to indicate that one cannot help doing something; cannot refrain from doing it.
彼の失敗を見ると、心配せずにはいられない。
When I see his failure, I can't help but worry.
あの歌を聴くと、涙が出ずにはいられない。
When I hear that song, I can't help but cry.
彼の冗談に笑わずにはいられなかった。
I couldn't help laughing at his joke.