A set of numbers is closed under an operation if the operation cannot be used with numbers from the set to get a number not in the set.

Can you add odd numbers together to get a number that is not odd?

Odd numbers are not a closed set under addition. Some examples:

$3+5=8,\ 3$ and $5$ are odd, $8$ is even
$7+13=20$, $7$ and $13$ are odd, $20$ is even
$15+15=30$, $15$ is odd, $30$ is even