A Clive Goddard cartoon from the January 2015 Funny Times:
On the left, a woman shopping for products to use during menstruation, euphemistically called sanitary products. On the right, an unsavory guy shopping for god-knows-what — but whatever it is, it’s unsanitary ‘unclean’.
Start with sanitary. From OED2, the root sense referring to health (Latin sanus ‘healthy’), later extended to cleanliness:
Of or pertaining to the conditions affecting health, esp. with reference to cleanliness and precautions against infection and other deleterious influences; pertaining to or concerned with sanitation.
At some point in the 19th century, the word was euphemistically extended to the menstrual context, presumably through the view that menstrual blood is unclean. The OED‘s first cite in this sense (from 1881, probably late) is for sanitary towel. Then came sanitary belt ‘a belt to which a sanitary towel is attached’ (1908), the specifically U.S. sanitary napkin (1917), sanitary pad (1926), and in 1936, sanitary protection ‘a collective term for the products (as tampons, sanitary towels, etc.) used by women during menstruation’. From Wikipedia:
A sanitary napkin, sanitary towel, sanitary pad, menstrual pad, maxi pad, or pad is an absorbent item worn by a woman or girl while she is menstruating, while she is recovering from vaginal surgery, for lochia (post birth bleeding), after an abortion, or in any other situation where it is necessary to absorb a flow of blood from her vagina.
