was is correct. because there was a significance to his remarks meant is incorrect because the significance doesn't mean anything. It's his remarks that mean something. The verb you choose needs to pair up with "significance" and "meant" isn't a perfect match. But even if you do use "meant" nobody will notice. Both sentences sound natural and nobody would care if you use meant or was.

Oops! I should have said: 1- We were unable to determine what his remarks really meant.

Sentence 2 is correct.

You could make the first one make sense if you worded it differently: 1- We were unable to determine what the his remarks really meant.