Celebrated: In the United States, origins obscure
If you find US-grown apricots in the supermarket, they almost certainly came from California. About 94% of the nation's apricots are grown in California, with most of the rest coming from Washington and Utah. They need a Mediterranean-style climate — long, dry summers and cool, wet winters — and did not thrive when English explorers brought them to the East coast in the 17th century.
They're one of the oldest cultivated fruits, so old that scientists aren't sure where they originated; I've seen claims for India, China and Armenia. Alexander gets credit for introducing them to Greece, but they're also mentioned in the Bible, and the "golden apple" that started the Trojan War might well have been an apricot. Today, most of the world's apricots are grown in Turkey, Iran and Uzbekistan.
Apricots are a stone fruit, of the genus Prunus, most closely related to plum. They're important to Chinese medicine, and medieval Europeans used dried apricots to treat constipation and induce labor (a plot point in The Duchess of Malfi). Their pits have measurable amounts of cyanide in them, though not enough to kill you unless you eat a lot of them. That cyanide is part of apricots' natural compound amygdalin, which some claim can be used to treat cancer; amygdalin is the basis of the drug Laetrile, banned by the USDA in 1977. The FDA calls Laetrile a "highly toxic product that has not shown any effect on treating cancer," and Steve McQueen died while on a Laetrile treatment program in Mexico.
This is not, of course, to say that apricots killed Steve McQueen.