Studenica Monastery is one of the WHS that means much more to the people of the nation where it resides than it does to outsiders. I went there with my Serbian friends while staying with them and it's a bit of trek to get to being somewhat buried in the Dinaric Alps.
The reason that the Serbian people revere this monastery is because it was founded by Stefan Nemanja, the founder of the medieval Serbian nation. It's an important site for Serbian people and that is very apparent when you're there.
The actual monastery comprises of the original Byzantine church and it's later extension plus some monastic buildings. There are important frescoes inside the church that have been sadly damaged during restoration work, this was the case when I visited in 2009, maybe they have been restored now.
I found it funny that an old monk said something to me in Serbian which made my friend laugh. I asked later what he had said and she said, "I wish you safe travels on your journey, unless you don't believe in God, then I don't care". Charming!