In the early 16h Century, a Franciscan friar, Matteo di Bassi, felt his order wasn't copying St Francis quite closely enough, and he tried to live more as he did. He grew a beard, went barefoot, lived liked a hermit, and preached to the poor. More important for my purposes, he designed a new habit -- same brown fabric as the Franciscans but now with a pointed hood.
This hood is cappuccio in Italian, capuche in old French, which comes from the Latin cappa, hood, and ultimately from Latin caput, head, which led to cape (like a cloak), cap (on your head), and to a lot of other words.
Anyway, others followed Matteo, dressing the same, and they got the French nickname capuchin, and cappuccino in Italian -- presumably, "little hood-wearer." After some internal Franciscan strife, the Pope allowed him to form a new order, a Franciscan offshoot named the Order of Friars Minor Capuchin, after their distinctive hoods.
When explorers came to the Americas, the saw a new species of small monkey that immediately reminded them of the monks -- with the pale face and a cap of dark hair atop the head, they called them Capuchin monkeys.
Another connection is of course the coffee drink, which seems directly connected but has two or three stories about how it came about. Most often, the color of the cappuccino reminding someone of the Capuchin robes -- but why not call it a Francisccino? Another says that the froth was pointed, and another that the foam sat on the top, like a monk's hood.
Also related to Latin cappa is chaperone. A chaperon was originally a hood for a hawk. From that sense, a verb chaperonner, to cover with a hood, or protect, and from there to an antique sense of an older woman who accompanied a young woman in public as her protector.
Further on, cappa as cloak brought us chapel, which was originally a very specific place: a place to hold the cape of St Martin of Tours, venerated by France's first kings. Latin for chapel was capella, and the a capella groups of today are merely singing in the manner of the choir in church -- without instruments.
