Actors rehearsing a play are, by the word's history, farmers dragging a harrow over a field they have already worked.
A harrow is a frame of spikes or tines pulled across plowed soil to break it up and level it. Old French called it a herse, earlier herce. Etymonline traces that word through Medieval Latin hercia to Latin hirpex, a rustic word for the tool.
From the noun came a verb, hercier, "to harrow." Add re-, "again," and you get rehercier, recorded in the 12th century. Etymonline glosses it as "to rake over, turn over" ground. The Saturday Evening Post's word column renders it as plowing a field again. The farming image is the same in every account: going back over ground you have already covered.
The French already used it figuratively for repeating something. English borrowed it around 1300 as rehersen, meaning to recite, narrate or report. By the mid-14th century it also meant to say over again. The theatrical sense, practicing a play in private before a public performance, is recorded from the 1570s.
The harrow left a second, gloomier word in English. French herse could mean a portcullis as well as a harrow. In English, hearse first meant a framework of candles hung over a coffin, so called because it resembled a harrow. The vehicle that carries a body to the grave took the name in the 1640s.
Folk stories cling to both words. A Grammarphobia reader had heard that rehearsal was a contraction of "re-hears-all," and the Saturday Evening Post column rejects a story about reburying a disinterred body. The two words are cousins because both descend from the same farm tool, not because one was built from the other.
There may be a wolf in the field, too. Etymonline says Latin hirpex is possibly from Oscan hirpus, "wolf," supposedly in allusion to the tool's teeth. That last step is a guess, but the harrow itself is well documented.