Why do Japanese celebrate Christmas?

Christmas celebrates the birthday of Jesus Christ. That is why we call this time of year 'Christmas' - we celebrate the 'Mass', or church service, for Christ.
The Word Christmas (or Christ's Mass) comes from the Old English name Cristes Maesse - Christ's Mass - and is the celebration of the birth of Jesus. The first recorded observance occurred in Rome in AD360, but it wasn't until AD440 that the Christian Church fixed a celebration date of 25 December.

middle class people gave little presents to their servants in boxes on Boxing Day.)