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It houses his medieval European Art - primarily church art.
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It is a beautiful setting. He purchased a lot of architecture that had been repurposed into farm houses after the French Revolution.
This is the Fuentiduena Chapel - a mid-12th century apse from the church of San Martin at Fuentiduena (Segovia).
The hanging cross is from the same period, but from Austria. It was amazingly pretty inside.
It is called "The Cloisters" because he actually took many cloister columns and used them to surround the gardens. Here is a picture of various types of columns from different cloisters around Europe.
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If you come and like this type of Architecture, Art or Gardens - you should go. It was spectacular.