St. Stephen's Day became a day when delivery men, errand boys and servants of various kinds expected to receive a gift. The term Boxing Day appeared in print as early as 1833.
There are several suggested origins. Which, if any, is correct, is unknown. A sort of servants - poor man's Christmas seems a likely origin, however.

Wasn't the turkey an American import, the goose and swan still the favorites through Victorian times?

COLD meat pie?