eligible
Qualified or allowed to do, have, or join something.
Eligible means qualified or allowed to do something, have something, or participate in something. When you're eligible for something, you meet the requirements or conditions necessary to be considered for it.
For instance, students might be eligible to join the school chess club if they're in fourth grade or higher. A family might be eligible for a library card if they live in the town. Athletes become eligible to compete in the Olympics when they reach a certain skill level and meet age requirements.
Being eligible doesn't guarantee you'll get something; it just means you're allowed to be considered. You might be eligible to run for class president, but you still need to campaign and win the election. A book might be eligible for an award, but judges still decide whether it wins.
You'll often hear people talk about eligibility requirements: the specific rules that determine who is and isn't eligible. Schools have eligibility requirements for the honor roll, sports teams have them for tryouts, and contests have them to make sure everyone competing plays by the same rules.
When someone isn't eligible, they're ineligible: perhaps too young, missing a needed qualification, or unable to meet some other requirement.