Nerve can be traced back all the way to the Sanskrit nauree, "string", circa 1000 BC, which gave rise to the Greek neuron, a term originally used by Hippocrates in the 5th century BC for various structures of a white, fibrous appearance, including tendons and ligaments ("sinews") as well as nerves; the word also was used for bowstring.
From neuron comes aponeurosis, first used by the Greeks for any broad, white, membrane-like tendon (apo is Greek for "derived from") and in use today for the same purpose. Examples include the epicranial aponeurosis and plantar aponeurosis.
In the 4th century BC, Aristotle restricted the use of neuron to the those structures we call nerves today. This was around the time the Greeks began to differentiate between the functions of nerves and sinews (they had come to realize that nerves were involved with muscle control, for example).
In one of the stranger quirks of anatomical etymology, Galen, in the 2nd century, came up with the word neuron, not from the Greek neuron, but from the Latin verb neuein, "to nod"; as he wrote: "nerves cause the limbs to nod and the joints to bend". Of course, he could have been simply enjoying a pun as well. However, it was the Greek neuron that gave way to the Latin nervus, which begat the French nerf, and finally the English "nerve".
Phrases such as "straining one's nerves" or "showing a lot of nerve" go back to the sinew notion of the word: strength, and from strength, courage.
Neuron, in the sense of a nerve cell, was coined in 1891 by the German anatomist Wilhelm Waldeyer, who first proposed the idea that the fundamental structure of nervous tissue was not that of a continuous web but rather discrete cellular units.
"Neuron" by Anna Vieth