The founder of Buddhism, Siddhartha Gautama was born in Kapilvastu city in what is now Nepal, exactly 2,553years ago. The remains of his palace can still be found in Kapilvastu, Lumbini, in Nepal. According to tradition, he was born under a tree which lies between his mother's home and his father's home. Some people believe that the tree is still alive in Kapilvastu and worshiped by pilgrims.
Siddhartha was a prince, but after learning of the suffering beyond the palace walls he became dissatisfied with his luxurious life. He renounced materialistic richness and practiced a number of ascetic spiritual disciplines, the deprivations of which, tradition has it, nearly killed him. Eventually he realized that a moderate "middle way" to spirituality was more logical, and discovered the process of inward meditation. By practicing this, he became "enlightened," meaning that he was able to discern reality, as opposed to the confusion that confounds most people's thoughts. The word Buddha simply means "enlightened one."
Buddhists consider the primary Buddhist teachings, the "Dharma" to be eternal, and that they were only discovered by Gautama Buddha.
In that sense, Buddhism did not originate anywhere. However, Siddhartha's insight and his teaching is, for practical purposes, the beginning of Buddhism. The traditional location where Siddhartha became enlightened is near a place known as Bodhgaya, and is a sacred place for Buddhists.
The Buddha (traditionally capitalized, as opposed to many other lowercase Buddhas) taught for forty to fifty years in the area of Northern India and Nepal. His students spread these teaching farther, transmitting them directly to their followers. Buddhist teachings today are based on the Buddha's Four Noble Truths and his expositions on those subjects, passed down by oral tradition as were the core teachings of most other beliefs. Some centuries after Siddhartha's death they were committed to writing in the Pali language, and later to Sanskrit.
Okay, this person's answer was very, very detailed, which is a plus. But as a Buddhist, I think I can provide a more personalized answer.
He was a man who found enlightenment by metatating for days. He found the middle way. We believe that if you give up all wants and desired, we can be like Siddhartha, the Buddha, the enlightened one, and find nirvana.