From the World Heritage inscription:
Built in A.D. 794 on the model of the capitals of ancient China, Kyoto was the imperial capital of Japan from its foundation until the middle of the 19th century. As the centre of Japanese culture for more than 1,000 years, Kyoto illustrates the development of Japanese wooden architecture, particularly religious architecture, and the art of Japanese gardens, which has influenced landscape gardening the world over.
If you can only visit one place in Japan, the place to visit is Kyoto. The former imperial capital of Japan, there are seventeen different temples, shrines and buildings in the Kyoto area which are included in the World Heritage property, and that technically doesn’t include the former Imperial Palace (which is still owned and run by the Japanese royal family) or the Fushimi Inari Shrine.
I’d suggest spending at least three days in Kyoto as the attractions are rather spread out and Kyoto is a large city. There are many other, smaller buildings of historical note throughout the city which might be worth visiting. Kyoto has a subway, so getting around is pretty easy.
View my complete list of UNESCO World Heritage sites.