A covenant is an agreement between two parties. In the Old Testament the Hebrew word translated covenant is the Hebrew word Berith which means to cut,. This is because in Old Testament times a covenant was ratified by cutting an animal into two parts and then both parties passing between them.
18 I will give the men who have transgressed my covenant, who have not performed the words of the covenant which they made before me, when they cut the calf in two and passed between its parts:
A covenant was a serious matter- and should never be broken. Most covenants we read of in the Bible are between God and man and for the benefit of mankind. For example God’s provision of day and night
God refers to his covenant that day and night shall not cease when talking about the Jews.
20 “The LORD says: ‘If you can break my covenant of the day and my covenant of the night, so that there will not be day and night in their time;
The rainbow is a permanent reminder that God would never again destroy mankind by flood:
13 I set my rainbow in the cloud, and it will be a sign of a covenant between me and the earth. 14 When I bring a cloud over the earth, that the rainbow will be seen in the cloud, 15 I will remember my covenant, which is between me and you and every living creature of all flesh, and the waters will no more become a flood to destroy all flesh. 16 The rainbow will be in the cloud. I will look at it, that I may remember the everlasting covenant between God and every living creature of all flesh that is on the earth.”