ability (n.)

"having sufficient power or means," early 14c., from Old French (h)able "capable; fitting, suitable; agile, nimble" (14c.), from Latin habilem, habilis "easily handled, apt," verbal adjective from habere "to hold" (from PIE root *ghabh- "to give or receive").

"Easy to be held," hence "fit for a purpose." The silent h- was dropped in English and resisted academic attempts to restore it 16c.-17c. (see H), but some derivatives (such as habiliment, habilitate) acquired it via French. Able seaman, one able to do any sort of work required on a ship, may be the origin of this:

Able-whackets - A popular sea-game with cards, in which the loser is beaten over the palms of the hands with a handkerchief tightly twisted like a rope. Very popular with horny-fisted sailors. [Smyth, "Sailor's Word-Book," 1867]

eighth letter of the alphabet; it comes from Phoenician, via Greek and Latin. In Phoenician it originally had a rough guttural sound like German Reich or Scottish loch. In Greek at first it had the value of Modern English -h-, and with this value it passed into the Latin alphabet via Greek colonies in Italy. Subsequently in Greek it came to be used for a long "e" sound; the "h" sound being indicated by a fragment of the letter, which later was reduced to the aspiration mark.

In Germanic it was used for the voiceless breath sound when at the beginning of words, and in the middle or at the end of words for the rough guttural sound, which later came to be written -gh.

The sound became totally silent in Vulgar Latin and in the languages that emerged from it; thus the letter was omitted in Old French and Italian, but it was restored pedantically in French and Middle English spelling, and often later in English pronunciation.

Thus Modern English has words ultimately from Latin with missing -h- (able, from Latin habile); with a silent -h- (heir, hour); with a formerly silent -h- now often vocalized (humble, humor, horizon, herb); and even a few with an unetymological -h- fitted in confusion to words that never had one (hostage, hermit). Relics of the formerly unvoiced -h- persist in pedantic insistence on an historical (object) and in obsolete mine host.

The pronunciation "aitch" was in Old French (ache "name of the letter H"), and is from a presumed Late Latin *accha (compare Italian effe, elle, emme), with the central sound approximating the rough, guttural value of the letter in Germanic. In earlier Latin the letter was called ha. The use in digraphs (as in -sh-, -th-) goes back to the ancient Greek alphabet, which used it in -ph-, -th-, -kh- until -H- took on the value of a long "e" and the digraphs acquired their own characters. The letter passed into Roman use before this evolution, and thus retained there more of its original Semitic value.