If something occurs in a strange or eerie way, you can say it happens mysteriously. Your little brother might mysteriously disappear every time the dog needs to be walked, for example.
When something can't be easily explained, it happens mysteriously. Some people say that boats mysteriously disappear in a region of the Atlantic Ocean known as the Bermuda Triangle, and others tell stories of sick people being mysteriously healed by prayer. At the heart of mysteriously is the noun mystery, which had only a religious meaning until the late fourteenth century, and which is rooted in the the Greek word mysterion, "secret rite or doctrine."