A covenant is a promise by the Lord about something He will do, or not do. He promised Noah that He would never again destroy the earth. And He promised Abraham that he would be father to a great nation. In some cases the promise was contingent on the people following His commandments, and not falling away to worship idols. The most often mentioned covenant was the one with Abraham that continued on with Isaac and Jacob and all the tribes of Israel.

(References: Arcana Coelestia 665, 1038, 1049, 1864, 2037, 8867)