Thumbelina is a tiny little girl, no bigger than your thumb. She is the main character in a fairytale story, also called Thumbelina (or Tommelise in original Danish), written by Hans Christian Andersen in 1835 and translated into English in 1846.
The story is very widespread. Many people know of Thumbelina, even if they do not know the origin of the story. Versions of the story have often been included in various fairy tale books, and will appear in the cheap animations you can buy for a buck in a dollar store. Danny Kaye sings of Thumbelina in the musical movie Hans Christian Andersen, released in 1952. The full length animated feature movie Thumbelina directed by Don Bluth and Gary Oldman was released in 1994, with a very catchy soundtrack. Thumbelina has even been given the Barbie movie treatment, released on DVD in 2009.
You can read the story of Thumbelina on E2, noded under the title Thumbelisa.