Horus was the god of the sky, and took the shape of a falcon, or a man with a falcon's head. Horus was also the son of Osiris and Isis, and in some pictures and statues he is shown as a child, often suckling at Isis' breast (see the picture right).
Horus was one of the first gods worshipped in ancient Egypt. His temple at Edfu (south of Luxor) is the best preserved in Egypt, although it dates from very late in Egyptian history.
By the way, if you see a falcon- headed god with a sun on his head, that is Re, not Horus.
Horus wears the double crown of Egypt on his head. This shows he is also god of pharaohs. Indeed kings were supposed to be Horus on earth. The crown has two parts: the red crown stands for lower Egypt (the Nile Delta) and the white crown stands for Upper Egypt.
In the myth of Osiris, Osiris was murdered by his brother Seth. Later on Horus fought an 80 year war with Seth to revenge his father. He eventually won and became king on earth. During this battle Seth tore our his eye. The eye was healed by Thoth, and so the Eye of Horus (or wedjat) came to symbolise wholeness. It was worn as an amulet to protect people against evil spirits (see bracelet below).