Why do they call it that?
Apparently nobody knows.
The holiday’s roots can be traced to Britain, where Boxing Day is also known as St. Stephen’s Day. Reduced to the simplest essence, its origins are found in a long-ago practice of giving cash or durable goods to those of the lower classes. Gifts among equals were exchanged on or before Christmas Day, but beneficences to those less fortunate were bestowed the day after.
And that’s about as much as anyone can definitively say about its origin because once you step beyond that point, it’s straight into the quagmire of debated claims and dueling folklorists.
Snopes: The Origins of Boxing Day