having the necessary qualities or satisfying the necessary conditions

Are you eligible for early retirement/maternity leave? 你符合提前退休／休产假的条件吗？

You might be eligible for a grant. 你或许有资格得到奖学金。

Only people over 18 are eligible to vote. 只有18岁以上的人才有资格投票。

An eligible person is not married and is thought to be a suitable future marriage partner, especially because they are rich and attractive.

I can think of several eligible bachelors of my acquaintance. 在认识的人当中我能想到有几位条件不错的单身汉。