What was meant when Jesus instituted the New Covenant at the Last Supper?

If you view the New Covenant as a legal document proposing a law then that law has to take effect from a certain date. Jesus did this when He said at the Last Supper "this cup which is poured out for you is the new covenant in my blood." (Luke Ch.22) So the New Covenant came into effect when the cup was poured out at the Last Supper. The new covenant is not a mere renewal of the earlier covenant that the Israelites broke. No, indeed! For the Apostle Paul writes to the Christians at Rome, saying: "You are not under law but under undeserved kindness." (Romans 6:14) It is really a new covenant, and it was to be expected that it would be a better one, for the Almighty God Jehovah is able to improve matters with regard to those whom he admits into the new covenant. For one thing, he raised up a better mediator, or go-between, in establishing the new covenant. This Mediator was no imperfect, sin-infected man like the prophet Moses. 8 The Law covenant mediated by means of the prophet Moses was good in itself. However, that covenant provided for the sacrifice of animals whose blood could never wash away human sins. So for Jehovah God to set up a better covenant, there would have to be a better mediator with a better sacrifice. This all-necessary Mediator proved to be Jesus Christ. Pointing out the superiority of this Mediator as compared to the prophet Moses, The Bible gives us the following explanation: "But now Jesus has obtained a more Excellent public service, so that he is also the mediator of a correspondingly better covenant, which has been legally established upon better promises. . . . In his saying 'a new covenant' he has made the former one obsolete."-Hebrews 8:6, 13. --Excerpt from "Insight on the Scriptures"