This pattern comes in paired phrases to indicate contrast.

- is interchangeable with verb +든지, verb +든지

Examples:
그걸 하거나 말거나, 난 몰라요./I don't care if you do it or not.
그 일응 마쳤거나 안 마쳤거나, 가야 합니다./Whether we finished that work or not, we must go.


Note: -거나 can attach to action verbs for a more generalized meaning of whatever, whoever, etc.
Ex: 누가 오거나, 괜찮아요./Whoever comes, it's alright.