I have heard this parable sliced and diced to represent branding, marketing, and customer perception. Here the original version from the Buddhist cannon:
A number of disciples went to the Buddha and said, "Sir, there are living here in Savatthi many wandering hermits and scholars who indulge in constant dispute, some saying that the world is infinite and eternal and others that it is finite and not eternal, some saying that the soul dies with the body and others that it lives on forever, and so forth. What, Sir, would you say concerning them?"
The Buddha answered, "Once upon a time there was a certain raja who called to his servant and said, 'Come, good fellow, go and gather together in one place all the men of Savatthi who were born blind... and show them an elephant.' 'Very good, sire,' replied the servant, and he did as he was told. He said to the blind men assembled there, 'Here is an elephant,' and to one man he presented the head of the elephant, to another its ears, to another a tusk, to another the trunk, the foot, back, tail, and tuft of the tail, saying to each one that that was the elephant.
"When the blind men had felt the elephant, the raja went to each of them and said to each, 'Well, blind man, have you seen the elephant? Tell me, what sort of thing is an elephant?'
"Thereupon the men who were presented with the head answered, 'Sire, an elephant is like a pot.' And the men who had observed the ear replied, 'An elephant is like a winnowing basket.' Those who had been presented with a tusk said it was a ploughshare. Those who knew only the trunk said it was a plough; others said the body was a grainery; the foot, a pillar; the back, a mortar; the tail, a pestle, the tuft of the tail, a brush.
"Then they began to quarrel, shouting, 'Yes it is!' 'No, it is not!' 'An elephant is not that!' 'Yes, it's like that!' and so on, till they came to blows over the matter.
"Brethren, the raja was delighted with the scene.
"Just so are these preachers and scholars holding various views blind and unseeing.... In their ignorance they are by nature quarrelsome, wrangling, and disputatious, each maintaining reality is thus and thus."
Then the Exalted One rendered this meaning by uttering this verse of uplift
O how they cling and wrangle, some who claim
For preacher and monk the honored name!
For, quarreling, each to his view they cling.
Such folk see only one side of a thing.
Of course, marketers don't have such patience to recite such a tale to an audience, so here is the watered down version of the parable:
One day, three blind men happened to meet each other and gossiped a long time about many things. Suddenly one of them recalled, "I heard that an elephant is a queer animal. Too bad we're blind and can't see it."
"Ah, yes, truly too bad we don't have the good fortune to see the strange animal," another one sighed.
The third one, quite annoyed, joined in and said, "See? Forget it! Just to feel it would be great."
"Well, that's true. If only there were some way of touching the elephant, we'd be able to know," they all agreed.
It so happened that a merchant with a herd of elephants was passing, and overheard their conversation. "You fellows, do you really want to feel an elephant? Then follow me; I will show you," he said.
The three men were surprised and happy. Taking one another's hand, they quickly formed a line and followed while the merchant led the way. Each one began to contemplate how he would feel the animal, and tried to figure how he would form an image.
After reaching their destination, the merchant asked them to sit on the ground to wait. In a few minutes he led the first blind man to feel the elephant. With outstretched hand, he touched first the left foreleg and then the right. After that he felt the two legs from the top to the bottom, and with a beaming face, turned to say, "So, the queer animal is just like that." Then he slowly returned to the group.
Related:
Wikipedia's take on this parable
US Peace Corps follow-up questions for the parable