The new year starts with an extra day off work (for most). The statutory Bank Holiday in Scotland is on the first day of the year, or the 2nd January or later if New Year's Day falls on a weekend.
Note that the 1st January is also a Council "Parking Holiday". You can park free of charge in public parking bays and on single yellow lines, although parking holidays do not carry over to the next working day. Bus lanes don't have parking holidays. It's one of four parking holidays in Edinburgh.