When I was a Buddhist i always understood Buddha and arahant as someone different to animals and ordinary human.
The story is called "Indra's lute".
Gautama was having difficulty deciding whether or not to give up the extreme austerities He had been practicing. Lord Indra comes to advise him.
Indra is seen with his lute-like instrument, which has three strings. He plucks one of the strings, which is too slack and makes only a dull sound. He plucks another string, but this one is too tight, and it snaps. The third string is properly tightened, and it makes a beautiful sound. In this way, Lord Indra encourages the Buddha to take the 'middle path', modifying his austerities so that His life will not be ended.
The slack string means surrendering to the animal nature, the string which is too tight stands for exaggerated, excessive striving for asceticism and "holiness" which is detrimental to health and well-being. If you have self-awareness and compassion with yourself, the "string" works properly and makes a nice sound.