Granny is a relation. She is either your Mummy's Mummy or your Daddy's Mummy. She may sometimes be known as Gramma or Granma.
A child was sitting with her mummy in front of me on the bus.She turned round to look at me and told me she and her mummy were going to visit her mummy's mummy. She then whispered softly, in the way littlegirls do when they want to tell you something really important "Mummy's Mummy is my Granny."