Indefinite means without clear limits or a definite end point. When your teacher says the playground will be closed for an indefinite period, she means there's no set date for when it will reopen. It could be a week, it could be a month: nobody knows yet.

Indefinite describes something vague, uncertain, or without fixed boundaries. A library book has a definite due date, like October 15th, but if the librarian says you can keep it for an indefinite time, there's no specific deadline.

In grammar, indefinite articles are “a” and “an,” called indefinite because they don't point to one specific thing. When you say “I saw a dog,” you mean some dog, not one particular dog you've already mentioned. That's different from “the dog,” which points to a definite, specific dog.

The opposite of indefinite is definite: clear, specific, and certain. When making plans, people usually prefer definite answers (“We're leaving at 3:00 PM”) over indefinite ones (“We're leaving sometime this afternoon”), because definite information helps everyone know exactly what to expect.