Updated: Dec 5, 2018
Kurma, the tourtoise, has 2 major appearances in Hindu mythology:
The fist is when Prajapati (Brahma), who wants to have a child, becomes Lord of the Waters - the tortoise, Kashyapa. All the matter of the universe is borne by his body and the world is supported by four elephants standing upon the shell of a turtle. Akupara is the name of the tortoise in Hindu legends who carries the world on his back upholding the earth and sea.
The second is one avatar of Vishnu (2nd) which is a giant turtle Kurma.The gods and the asuras (demons/titans) cooperated in the churning the water to obtain amrita, the elixir of immortality from the ocean. The great serpent Vasuki offered himself as a rope, and Mount Mandara was torn out for use as a churning stick. A firm foundation was required to steady the mountain, so Vishnu took the form of a tortoise and supported the churning stick on his back.
Turtles are a popular symbol in mythology because of their longevity and appearance. They are also symbols of the more tranquil and protective aspects in the mythology. The withdrawing action into their shell represents the meditative state.
Krumasana is not just imitating the shape of a tortoise but also creates the shape of complete folding in which facilitates the withdrawal of our senses, tuning inward. It is definitely not a meditation pose however in it you have to face yourself and if you allow for few breaths the complete surrender you can not just face and feel, but also find yourself.