Final answer:
In 1636, the significant event associated with Harvard University was its foundation, marking the start of this esteemed institution as the first university in what would become the United States.
Step-by-step explanation:
The significant event that occurred in 1636, associated with Harvard University in Massachusetts, was the foundation of Harvard University. This institution was established as part of the commitment of the Puritans to education, which they deemed essential for religious understanding and salvation. Harvard University played a pivotal role in early American education, as it was the earliest institution of higher education in the United States and has since become one of the most prestigious universities worldwide.