The son of Iapetus and Clymene, Prometheus' name means 'foresight.' It was this foresight that allowed him to choose the side of the Gods in the Titanomachy. Therefore, Prometheus, along with his foolish brother Epimetheus, were spared from languishing in Tartarus.
After Zeus became king of the universe, Prometheus began creating problems for him. The first offense was that Prometheus refused to tell Zeus of the prophecy that one of his own children would overthrow him as king.
The rest of Prometheus' conflict with Zeus revolves around the evolution of mankind. Some stories say that Prometheus actually created mankind from the soil, but all have Prometheus as the champion of mankind. After the end of the Golden Age, and other the other successive ages, mankind was struggling to barely survive upon the earth. Prometheus, however, decided to personally aid the poor creatures. Prometheus tricked Zeus into taking the unwanted portions of the sacrificed animal, instead of the meat. He arranged this by wrapping the bones of the animal in the glistening fat, while laying the smaller portion of meat to the side. Prometheus bade Zeus to choose which portion should be his, and he chose wrong. It was for this reason that the Greeks rationalized their sacrificing of the inedible portions to the gods, while keeping the meat for themselves. Prometheus also stole fire from Olympus to aide them as well.
Finally, it was Prometheus who placed hope inside the jar/box of Pandora, preventing mankind from being overrun by the evils of the world. These actions of Prometheus earned him the title of 'savior of mankind.'
Zeus, enraged by the cunning deceit of Prometheus, chained him to a to a mountain, usually identified as the Caucasus. Everyday, an eagle flew down and fed upon his liver, which would regenerate again that night. Zeus decreed that Prometheus would be freed only when he revealed the secret of which offspring of Zeus would overthrow the great king.
This cruel punishment was finally ended by Zeus' son Heracles. Although still angry at Prometheus, Zeus was willing for this transgression to pass so that the fame of his son might be even greater.
Hesiod. Works and Days.