Who is the object of the New Covenant and what are it's terms?

I've asked this question to several people over the years, only professing Christians and particularly those who tout them selves as 'New Testament Christians'. And this is an important question as Mathew 26:28 tells us that this is the Covenant offered in Christs very own blood: Mat 26:28 For this is my blood of the New Covenant (testament), which is shed for many for the remission of sins. Any one with apt comprehension can identify the parties to this Covenant as quoted in Hebrews 8 and Jeramiah 31, yet even more so for some one with legal background such as a contract lawyer the party and terms here specified are clad tight: > Jer 31:31  Behold, the days come, **saith the LORD**, that I will make a **new covenant with the house of Israel, and with the house of Judah**:  Jer 31:32  Not according to the covenant that I made with **their fathers** in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the LORD:  Jer 31:33  **But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law** in their **inward parts, and write it in their hearts; and will be their God, and they shall be my people.  Jer 31:34  And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.**  > Jer 31:35  Thus saith the LORD, which giveth the sun for a light by day, and the ordinances of the moon and of the stars for a light by night, which divideth the sea when the waves thereof roar; The LORD of hosts is his name:  Jer 31:36  If those ordinances depart from before me, saith the LORD, then the **seed of Israel** also shall cease from being a nation before me for ever.  Now this is repeated in Hebrews 8, as I had said. By expository bible study and exegeting this text to understand what Christ is affecting in his blood what do you all arrive at for the what, who, why, and how?