Zelda series producer Eiji Aonuma wanted to remake Ocarina of Time to help younger members of the development team gain new insights, he explained in a recent article on the official Nintendo website. Aonuma worked on the original N64 version of the game and wanted to task the team with remaking it to mark the series' 40th anniversary.
He hoped that those who didn't work on the N64 version would learn aspects of the game's development that they could apply to future Zelda titles. Aonuma wanted the team to learn from the original game's structure and development style, and to rebuild it as a full remake to trigger new insights. He gave the team freedom to decide which elements of Ocarina of Time to keep and which to change, and was surprised to see how few changes they actually made.
Aonuma was impressed by the team's ability to craft a rich experience from a game that first came out 28 years ago.