To be ineligible is to not qualify for something.
When you're eligible for something — like a contest — you are allowed to enter. Being ineligible is the opposite; it means that you can't enter or participate in something. After a certain age, children are ineligible for playing Little League baseball. Students below a certain grade point average are ineligible for scholarships. People born outside the United States are ineligible to run for President. If you want to know who's eligible and ineligible for something, check the rules or laws.