Anna had always wanted to be buried at Castle Seeon in Germany, a place she stayed in the 1920s with one of her biggest supporters, the Duke of Leuctenberg. She thought it was beautiful and a nice place to rest, I suppose. It's not a place where royalty are known to be buried, there are no other Romanovs there, so it's nothing special in that way for her to be there.
When she died in 1984, she was cremated, and it's only her ashes which are buried there. Some found it strange she requested cremation since if she had been Anastasia she'd have been raised in the Orthodox church she'd have been opposed to it. That is why many people believe she wanted to be cremated so that no tests could ever be done on her body to prove her a fake. She was cremated almost immediately after death due to her requests. The DNA tests, performed ten years after her demise, were done on a piece of intestine stored at the hospital where she had surgery in 1979.