As you pointed out, the standard Roman year was 355 days long. Every couple of years they added another intercalary month to February. The job of determining when to do this fell to the high priest (*pontifex maximus*). The problem was, either for political reasons, civil unrest, or what have you, they sometimes didn’t. Caesar, during the Civil War, was himself *pontifex maximus*, and was a little busy. So the year had drifted quite badly.
By 46BC the winter festivals were occuring in the Fall, the Fall festivals in the Summer, and so on. In order to get them back to the proper season, Caesar, as part of his calendar reforms, added days at the end of February, as well as before and after December.
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