Eating fruit keeps you healthy.
According to 'America's Popular Proverbs and Sayings' by Gregory Titelman, this expression was first found as a Welsh folk proverb in 1866: 'Eat an apple going to bed, and you'll keep the doctor from earning his bread'.
However, I wonder if it it's root isn't further back in time, and that the expression is not simply saying that apples/fruit keep you healthy, but alluding to the apple as a symbol. For example, in ancient Irish tradition the apple symbolized immortality, and many traditions have believed the apple to be a symbol of love and fertility, even the preferred food of the gods - if you cut an apple in half across the middle you'll see that the core forms the shape of a five pointed star/pentagon - a shape that has been revered for millennia as having spiritual qualities.
More about apples:
Pythagoreans, in ancient Greece, gave apple as gifts because of their pentagon shaped core.
Traditional Christianity often refers to the fruit of the Tree of Knowledge as being an apple.
Apples have long been associated with divination: these are some of the many traditions:
Bobbing for apples (trying to retrieve an apple using only ones mouth from a tub of water) was originally a boys game - the girls prepared the apples and the boys would bob for them, the apple that each boy retrieved indicated who they would marry.
Peel an apple in one piece, throw the peel over your shoulder and the shape that the peel falls in indicates whether the answer to the question should be yes or no.
If your question is about love, take a pip from an apple, state the name of your loved one, throw the pip in the fire, and if it pops it indicates that the love is reciprocated!
Alphabetical list of expressions
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The idiom “to kill two birds with one stone” is used to describe achieving two objectives at the same time. The term references a common hunting tool, the slingshot; slingshots continue to be used to hunt small birds, and at one point, they were very common. As you might imagine, killing one bird with a stone requires an excellent aim and control over the slingshot; to kill two could be considered even more difficult, a task for only the most skilled of hunters. This idiom dates from the 1600s, and it was initially used in a somewhat pejorative way, to describe a philosopher’s attempt to prove two arguments with a single solution. The implication was that killing two birds at one time is extremely challenging and unlikely, and that the philosopher’s attempt should be viewed with extreme suspicion. The philosopher had obviously failed to satisfy his critics, who suggested that his attempt was about as successful as a try to knock out two birds with a single stone.
Over time, “to kill two birds with one stone” has come to be used more generally to accomplishing two goals at once, and the negative connotations have largely vanished. In fact, people are encouraged to think of ways to accomplish it, thereby living much more efficient lives. This is especially true in the business world, where employers are constantly on the hunt for ways to cut costs and improve efficiency, so something that kills two birds with one stone could be quite useful. For example, someone could be flying to a city on business, and decide to visit a family member while he or she is in the city, or a company might have an employee pick up a shipment somewhere while he or she is already there.
From the point of view of both the employee and the company, this can be convenient, because the employee will be reimbursed for mileage and other expenses, while the company can save a trip. Some people feel that this term is a bit negative, given the association with hunting and death, and they prefer more positive twists on the saying. Several organizations have even sponsored contests to come up with a new and more animal-friendly version of “to kill two birds with one stone.” However, the idea has become so entrenched in many societies that it is unlikely to fade from usage anytime soon, negative or not.