Dot was a girl living on the streets of nineteenth-century London.
During the frost fair of 1814, Sutcliffe's men paid Dot and other homeless children to lure people to the fair on the frozen River Thames to be fed to the creature he had trapped underneath.
The Twelfth Doctor later modified Sutcliffe's will and made Dot and the other orphans his heirs, allowing them to live inside his mansion. (TV: Thin Ice)