Indefinitely means for an unknown or unlimited amount of time, with no clear endpoint. When a library closes indefinitely, officials don't know when it will reopen: maybe in a month, maybe in a year, maybe never. When your parents say you can keep playing outside indefinitely, they mean until something changes, without setting a specific time to come in.

This doesn't always mean forever. A road might be closed indefinitely while engineers figure out repairs, but it will eventually reopen. A subscription might renew indefinitely until you cancel it. The key idea is uncertainty about when something ends, not that it never will.

People sometimes confuse indefinitely with infinitely, but they're quite different. Infinitely means actually endless, like the number line in math. Indefinitely just means the end point isn't known yet. When a store postpones its opening indefinitely, frustrated customers wish the owners would just pick a date.