The word “testament” also means “covenant.” These may seem like scary words because they are not used in modern English. They refer to a contractual agreement between two parties (in this case, God and man).
In the Old Testament, God makes a number of covenants with man. God promises Abraham that through Abraham, the people of the earth would receive blessings (Gen. 22:18). God also promises the Israelites blessings for obedience (Deut. 28:1-2). God promises David a king to sit on his throne forever (2 Sam. 7:12).
All of these covenants find their fulfillment in the New Testament (covenant). Jesus comes from the line of Abraham, and the earth is blessed through Jesus Christ. Jesus fulfilled the law of Moses perfectly. Jesus is also from the line of David and is the Promised One who will sit upon David’s throne as King.
Simply put, the New Testament is the fulfillment of the Old Testament