In 1683, Jacob Bernoulli was working on a problem with regard to compound interest. In calculating compound interest, the formula comes down to (1 + 1/n)n. Bernoulli noticed that this equation had a limit between 2 and 3 as n got larger and larger.
Today, we would state the definition for Euler's Number in the following way:
e = 2.7182...
This value is called Euler's Number after Leonhard Euler. Euler refered to the constant as "e" in 1727. He was not the first to discover the constant but he published so many important mathematical works relating to e that it became known as Euler's Number. Interestingly, it is believed that Euler chose "e" not because it was the first letter of his last name but because he wanted to use a vowel and he had already used "a".
Here is a graph of ex: