What was the significance of the Battle of Leyte Gulf?

I would say it represented the last nail into the coffin of the Japanese Imperial Navy.

The battle was a strategic defeat for the JIN because didn't fulfill its objectives of destroying the invasion landing and logistic forces for the invasion of the Philippines.

Not only this: it was a massacre for the air force as well as for the navy: many irreplaceable ships were either damaged or sunk and a huge number of pilots never returned from the useless attempts to attack the American Forces.

It is indicative of the tiredness and lack of enthusiasm of the Japanese commanders that Admiral Kurita at the exact moment, at Samar, of being near to destroy the escort ships and so be able to fulfill its mission, decided to withdraw!