What does Boxing Day have to do with boxing?
late 14c., "capable of sensation or feeling;" also "capable of being sensed or felt, perceptible to the senses," hence "easily understood; logical, reasonable," from Late Latin sensibilis "having feeling, perceptible by the senses," from sensus, past participle of sentire "perceive, feel" (see sense (n.)). Of persons, "aware, cognizant (of something)" early 15c.; "having good sense, capable of reasoning, discerning, clever," mid-15c. Of clothes, shoes, etc., "practical rather than fashionable" it is attested from 1855.
Other Middle English senses included "susceptible to injury or pain" (early 15c., now gone with sensitive); "worldly, temporal, outward" (c.1400); "carnal, unspiritual" (early 15c., now gone with sensual). Related: Sensibleness.
sensible sen·si·ble (sěn'sə-bəl)
Perceptible by the senses or by the mind.
Having the faculty of sensation; able to feel or perceive.
Having a perception of something; cognizant.