What does Boxing Day have to do with boxing?
Old English felt, from West Germanic *feltaz "something beaten, compressed wool" (cf. Old Saxon filt, Middle Dutch vilt, Old High German filz, German Filz, Danish filt), from Proto-Germanic *felt- "to beat," from PIE *pel- "to thrust, strike, drive" (cf. Old Church Slavonic plusti), with a sense of "beating" (see pulse (n.1)).
"to make into felt," early 14c. (implied in felted); see felt (n.).
past tense and past participle of feel (v.).