Nut held up by her father, Shu. Geb can be seen reclining on the ground. From "Egyptian Mythology" by Veronica Ions.

Nut, identified only by the hieroglyphs above her head, on the ceiling of a recently discovered tomb. Taken by the renowned Egyptologist, Dr. Hawass. (http://www.drhawass.com/photoblog/image-goddess-nut-tt11)

A note on Incest

In ancient Egypt, incest was a very common occurrence in both mythology and royal tradition. Just as the gods married and procreated with their siblings and parents, so did the pharaohs of ancient Egypt. The purpose of this was to keep the royal bloodlines pure. While it may come as shocking and revolting to modern readers, incest was really quite commonplace in the ancient world.

Nut: Other Associations

Nut is associated with other worldly things. She and her daughter Isis are equated with the sycamore tree. Many coffins were constructed from sycamore wood for even more of Nut’s protection. Nut is also identified with the number nine, mainly because of her inclusion in the Heliopolitan ennead: Atum, Shu, Tefnut, Geb, Nut, Osiris, Isis, Set, and Nephthys. Another, more obvious connection is with the color blue (irtiu/khesbedj). Ancient Egyptians held that the color blue symbolized water and the heavens, but, since water can also be represented by green, mainly the heavens. Yellow is considered another heavenly color, mainly of the sun and stars. 

A note on Cosmogonies

In the ancient Egyptian tradition, there are four central cosmogonies: the Heliopolitan cosmogony, the Memphite cosmogony, the Hermopolitan cosmogony, and the Theban cosmogony. While these are the primary accounts of mythological tradition, there are countless other cosmogonies that have not yet been named. I, as a very opinionated, albeit novice, scholar of Ancient Egyptian culture, prefer the Heliopolitan cosmogony.

Nut: Guardian of the Dead

The goddess Nut plays a very important role in the order of the world. Every single morning, she gives birth to the sun. This newborn, resurrected sun is known as the god Khepri. He is often represented as a scarab beetle. The resulting blood turns the sky pink as the sun rises. When night begins to fall, it is said that Nut swallows the sun, so that he might be born again at dawn. Because of her affiliation with Khepri, Nut is also associated as the Protector of the Dead. It is held that the dead become stars on her body. For this reason, she is often painted on the inner lid of sarcophagi, in hopes that the dead will be protected.

A sarcophagus depicting Nut.
(http://brunelleschi.imss.fi.it/galileopalazzostrozzi/object/SarcophagusLidPortrayingTheGoddessNut.html)

A picture from "Egyptian Mythology" by Veronica Ions.

Nut: Lineage and Issue

In the Heliopolitan cosmogony (which, unless otherwise mentioned, will be used as the source), Nut was the daughter of Shu and Tefnut. Shu, the god of Air, was created when his father, Atum, spit him out. Tefnut, Shu’s sister, was the goddess of Moisture. She was created when Atum vomited her forth. Atum was a self-creating god, often given the epithet “He who created Himself”.

Nut’s consort was her twin brother, Geb (Keb), the god of the earth. He was often referred to as “The Great Cackler”. It is said that, before the creation of the universe as we know it, the two of them lay in an embrace of sexual union. Ra, the Sun god, was greatly vexed, maybe even jealous, of the couple. He ordered Shu to separate them by holding Nut up so that only her fingertips and toes touched the earth. 
Ra also prohibited Nut from marrying Geb; when she disobeyed, he decreed that she would never bear children in any month of the year. The Moon god, Thoth, felt sorry for Nut and gambled with the moon; he won from the moon “a seventy-second part of his light.” In doing so, the five days before the Egyptian new year (called the days "above the year") were created, and Nut bore a child on four of them. Traditionally, the order of her children is as follows: Osiris (Ausar), Isis (Eset), Set (Seth), and Nephthys (Nebhet). (While there are some stories that hold the god Horus/Heru was also born of Nut, this contradicts the accepted tradition that his parents are Osiris and Isis.) 
Nut is said to have numerous other children, and is sometimes (as previously mentioned) depicted as a sow, her great belly providing milk to countless piglets, the stars. Tradition holds that she swallows her children every morning, presumably birthing them again at dusk. 

Nut: Overview

Nut in
Hieroglyphs

Nut is identified by the water
pot balanced on her head.

Nut (pronounced Noot) is the Sky Goddess in Ancient Egyptian Mythology.  Nut is also referred to as Neuth and Nuit. Nut, like almost all other gods, had skin of pure gold, bones of pure silver, and hair of real lapis lazuli. She was most often portrayed as a woman with a very elongated body, arched over the earth. The ancient Egyptians sometimes envisioned her as a great cow or sow with stars in her belly, standing over the earth. When she is depicted in "human" form, she can be identified by the waterpot or womb placed on her head.

This papyrus scroll depicts Nut and her consort Geb (the Earth god)
being seperated by their father, Shu (the Air god). Taken from "Egyptian Mythology" by Veronica Ions.

She is considered the mother of four very important deities: Osiris, Isis, Set, and Nephthys. In some traditions, Osiris and Isis conceived their son Horus while still in the womb. 


(Note: The image of Nut seated on a throne can be found at http://www.egyptianmyths.net
As for the sources of my information, I have used and will use: "Egyptian Mythology" by Veronica Ions and "Symbol & Magic in Egyptian Art" by Richard H. Wilkinson, as well as the splendid website egyptianmyths.net
 I have also drawn heavily from personal knowledge. I began studying ancient Egypt as a small child, and so some of the information is from my own memory.)