Jeremiah 31:31
ESV - 31 Behold, the days are coming, declares the Lord, when I will make a new covenant with the house of Israel and the house of Judah.
The previous answer was fantastic. I only want to offer these supportive and additional insights into the concept of New Covenant: ““Behold, the days are coming, declares the Lord, when I will make a new covenant with the house of Israel and the house of Judah…” “For this is the covenant that I will make with the house of Israel after those days, declares the Lord: I will put my law within them, and I will write it on their hearts…” Mouse over this link and read the entire passage of Jer. 31:31-34 afresh. Jeremiah and the book of Hebrew quoting Jeremiah (Heb. 8:8; Heb. 8:13; Heb. 12:24) are the only places in the Bible that mention “New Covenant.” Also, it is said to be made only with Isra'el and Judah (later in Jer. 31:33, only Isra'el). This tells me that the Church must exist as a part of Remnant Isra'el in order for her to participate in the New Covenant. There are not TWO new covenants, one with Isra'el and one with the Church, right? Moreover, Jeremiah says that the Torah (the Law of Moshe) is the written essence of this single New Covenant that the people of Isra'el took on as a never-ending agreement with God, and is that which will be written on New Covenant hearts. Yeshua (Jesus) said, "Not one stroke of the Torah will pass away until all is fulfilled" (Mat. 5:18), so this “new covenant” must be an internalization of the very same Torah, and built upon the previous covenantal promises. Unless we have gotten to the point yet of needing no one to teach us, the Torah is still in effect. All Scripture must be interpreted to agree with it (Isaiah 8:20). God does not change his mind. The nature of human sin demands the remedy called “new covenant.” The problem lies with unsaved mankind characterizing [concepts of] the Torah (viz, for unsaved Jews: ethnicity; for unsaved Church attendees: obedience or Church membership) as a means of justification in opposition to genuine submission to the Spirit of God. Pride and sin harden the heart, blind the eyes, and eventually make God’s gracious promises seem useless to unbelievers on a genuine spiritual level, leading to what Paul describes as “old covenant” in 2 Cor. 3:14. In this scenario, the covenant-member candidate may look spiritual but is actually fooled into thinking that mere mechanical allegiance to the Torah or superficial membership in a Church or Isra'el will provide a remedy for the sins piling up in his spiritless life. Mankind is in desperate need of the New Covenant whether he knows it nor not! Conclusions: The word "new" in the covenant spoken about in Jeremiah is actually the Hebrew word "chadashah," which can at times refer not to something brand new in creation but rather something that has undergone a reformation in character and purpose, or a simple refreshment on a different scale. On one level Jeremiah is describing a “renewal” of some existing item. On the other hand, when it comes to the regeneration of the soul of a man, viz, “old covenant” man vs. “new covenant” man, the change is quite radical: all things do indeed “become new.” Behaviorally speaking, the change can at times seem to occur over the course of time, but forensically speaking, the change is as different as life and death! The New Covenant to be ratified on a national level with Isra'el will envision the former promises made with Abraham, Moses, and David. It is not necessary to overturn a previous covenant in order for a later one to find fulfillment. To be sure, Galatians teaches explicitly that a later covenant cannot nullify a previous one (see Gal. 3:17). As a feature of the living Word of God, the new covenant is not time-bound. Rather, the new covenant springs to life whenever the veil is lifted and eyes are opened to God’s Grace, specifically as has been historically demonstrated by the coming of his Son. It is better in many, many ways since Yeshua himself in fact inaugurated it before the foundations of the world were even laid.