Yes the post office is open on Christmas Eve.
The post office will deliver mail and other packages on Christmas Eve and will then close on Christmas day.
Then the USPS post office will open and resume operations and mail delivery the day after Christmas day.
But Christmas Eve the post office is open but not on Christmas day.
So if you have any mail to send you should send it on Christmas eve but if you have mail to send that you need to arrive by Christmas eve you need to mail it at least a week before Christmas Eve because of the holiday rush.
The USPS gets backed up on mail during Christmas holidays so it's best to send the packages as soon as possible so that it arrives on Christmas Eve or before.