Why Boxing Day?
The 26th of December is the Feast of Stephen (the first Christian martyr) and is referred to in the carol Good King Wenceslas. In the church calendar, St Stephen's Day is associated with alms: collecting money for the poor
In England, parish churches would alms boxes would be brought into the church during December. They alms boxes would then be broken open on Stephen's Day. Pepys refers to this in his diary entry for 19 December 1663.
Thence by coach to my shoemaker’s and paid all there, and gave something to the boys’ box against Christmas
The day also became associated with recreational and sporting events. These included chaotic 'football' matches between villages. By the Nineteenth Century this had evolved into a secular festival for workers. The name Boxing Day was made official in the 1830s and became a public holiday in the 1880s.
In Catholic Ireland there are distinct traditions associated with 'Stephen's Day' - see here.