Can someone tell me what started means

Started, but not yet finished and filed.

Do I need to do anything else

OK ... did you efile the federal & state return at the SAME time ?   If so the state will remain in the STARTED status until the federal is either accepted or rejected.   If accepted the state will be filed automatically.

My federal got accepted. So I don't have to do anything else? This is my first time doing my own taxes

If you sent them together you should be good ... but log in & check.  Click on the state tab and then the Review tab and finally the FILE tab.

It doesn't give me that option when I log in

I’m having the same issue. This didn’t happen to me last year either,

To open a closed return scroll down and click on "ADD A STATE" to unlock the program ... then you can click on the state tab and then the Review tab and finally the FILE tab.