An apricot is, by name, a precocious fruit. Both words grow from the same Latin idea: something that ripens before its time.
The Romans described the fruit as praecoquum, "early-ripening." The usual explanation is that they saw it as a kind of peach that ripened ahead of the others. The Latin breaks into prae, "before," and coquere, "to cook" or "to ripen," as if the sun had cooked it early.
What makes the word unusual is the route it took next. Greek borrowed the Latin as praikokion, and Byzantine Greek wore it down to berikokkia. Arabic took the Greek word and fixed its own definite article to the front, giving al-barquq. When the Arabic word entered the languages of Iberia, the article came with it, producing Catalan abercoc and Portuguese albricoque. A Latin word had left Europe and come back with an Arabic "the" glued on.
English picked it up in the 1550s as abrecock. The fruit itself had been introduced to England only a few decades earlier, in 1524. Over time the spelling drifted toward the French abricot, which supplied the final t. Some dictionaries have suggested that the shift from abr- to apr- was nudged by Latin apricus, "sunny," which suits a fruit that loves warmth. The linguist Anatoly Liberman treats that as possible but unproven. Either way, the sunny look-alike is not the real source.
The older Latin name tells a different story. Romans also called the fruit prunum Armeniacum, the "Armenian plum," because they believed it came from Armenia. Botanists kept the idea in the species name Prunus armeniaca. Genomic research does not support it. A study reported by France's agricultural research institute, INRAE, found that both European and Chinese apricots were domesticated from wild populations in Central Asia.
The cooking verb behind praecoquum has a large English family. The same ancient root for "cook, ripen" sits behind cook, kitchen and biscuit, so an apricot shares a distant ancestor with the oven.