The infringed technologies are what allow data to be stored in a stream of sorts, and enable the tile-swiping on the iPhone and other Apple products. The original patents were filed by Yale professor and Mirror Worlds founder David Gelernter in 1999.
Apple doesn't seem to be contesting that they use the technologies, but they are claiming that the patents are being extremely overvalued. Apple chief counsel Jeffrey Randall says that the patents have already been sold twice before for $5 million.
Apple is filing for an emergency motion, hoping to reduce the settlement amount. Randall argument says that Mirror Worlds is "triple-dipping", charging $208.5 million per patent.