The Paleo or Paleolithic diet is based on the premise that we should go back to eating the way that cavemen used to eat — namely only plants and animals. The Paleo diet focuses on grass-fed pasture raised meats, seafood, vegetables, fruits, and nuts, and excludes grains, legumes, dairy, refined sugar, and processed oils. The Primal diet is basically the Paleo diet except it allows for the consumption of raw dairy.
These posts detail raising a Paleo family as well as Paleo-friendly recipes.