The word “covenant” is from the Latin word “con venier” which means to come together. The Old Testament word for covenant meant a binding between two parties. This “coming together” involved agreeing to a promise with stipulations, privileges, and responsibilities. Two important ones in Genesis and Exodus are the Abrahamic covenant and the Mosaic covenant.
In Hebrews 8, the author makes it clear that a new covenant is at hand. The Mosaic covenant God made in the wilderness with the ancient Hebrews was now being replaced with a new covenant where Jesus Christ was the mediator. This was monumental to the ears of a Christian Jew at the time of Jesus. Their entire society functioned under the Law of Moses and the sacrificial system set up in the old covenant.
In chapter 9, there is a look back to the Tabernacle and specifically the Holy of Holies and comparing it to the throne room of God.