According to prophecy, the "House of Israel" and the "House of Judah" will walk together to the land that is given as an inheritance from God (Jeremiah 3:16-19). Prophecy foretold a New Covenant would be established for the House of Israel and the House of Judah, which will be different from the former covenant (Jeremiah 31:31-32).
HOUSE OF ISRAEL
We are all sons of God through our faith in Jesus Christ (Galatians 3:26), because all who have been baptized into Christ (Matthew 28:19) have put on Christ (Galatians 3:27). These Scriptures reflect one another, for since Christ is the son of God (Mark 3:11, John 1:34), and we are sons of God as well, this would make us brothers to Christ. Connecting this further, Scripture states God would declare the people of the nations righteous due to faith. This is why God told Abraham "All nations shall be blessed in you "; this is because those who adhere to the faith are considered sons of Abraham and are being blessed accordingly (Galatians 3:7-9).
According to biblical history, the physical nation of Israel was collectively the sons of Abraham (Genesis 17:19, 21:12, 25:21-26, 32:28). Therefore, we who are sons of God, (Christ's brothers), are spiritual "Israel" since we are spiritual "sons" of Abraham as well. This blessing of Abraham was to be accomplished through Christ for the nations that we might receive the promised spirit through our faith (Galatians 3:14). Along with this, the Bible tells us that Christ is Abraham's "seed" (Galatians 3:16) and all who belong to Christ are also the "seed" of Abraham, heirs with reference to a promise (Galatians 3:29).
HOUSE OF JUDAH
Putting it all together: Adherents to faith are spiritual sons of Abraham, and thus are spiritual Israel. God will choose some from out of them to make up the royal spiritual House of Judah to rule over the House of Israel.
We have seen that the two Houses, Israel and Judah, are related. According to prophecy, the covenant to be made with Israel is this: God would put His law within them and their hearts; He will become their God and they will become His people, and all will know God and He will forgive their sins (Jeremiah 31:33-34, Hebrews 8:10). Knowing that covenants must be inaugurated by blood (Hebrews 9:18, 20-22), Christ said that this New Covenant was to be started through his blood, which was symbolized by the wine at the Last Supper (Luke 22:19-20). We know that Christ's death is the inauguration of the New Covenant because he called it the "blood of the New Covenant" (Matthew 26:28, Mark 14:24, Luke 22:20).
Thus, Christ pouring out his blood for us is the beginning of the New Covenant intended for both the House of Israel and the subset House of Judah. Paralleling this is 1 Corinthians 11:23-26, which states that eating the bread and drinking the wine is symbolic of proclaiming Christ's death for us until he returns. The shedding of his blood makes Christ the mediator of this New Covenant (Hebrews 12:23-24), and this makes Christ the sole mediator between God and men (1 Timothy 2:5-6).
Christ needed to mediate this New Covenant in order to release people from sin, so that a kingdom covenant with Judah could be carried out. (The Kingdom Covenant is addressed under the next subheading) This New Covenant was necessary in order to cleanse us from sin, otherwise there'd be nobody spiritually clean enough to be chosen for the Kingdom Covenant made with the House of Judah. Only after this cleansing occurs can anyone be chosen for Judah, which is pointed out at Hebrews 9:15. The New Covenant releases us from the old Law Covenant of the ancient Israelites, and allows those who are called into the House of Judah to receive the Kingdom (Hebrews 9:15-22). This means that since we are all under this New Covenant, we are all under Christ's mediatorship and his blood for forgiveness of sin. This New Covenant makes the former covenant obsolete (Hebrews 8:13).
Because this Kingdom Covenant was spoken of after the revealing of the New Covenant, after the bread and wine was consumed, and after other conversation, we know that this Kingdom Covenant is a separate thing from the New Covenant. Supporting this is the fact that Christ states it is he that is making this Kingdom Covenant with them (Luke 22:29-30) (KJV, NIV, CEV), whereas the New Covenant was originated from Jehovah/Yahweh, the Father (Jeremiah 31:31 - Darby) (NASB, YLT), showing these are two separate covenants dovetailing together.
This Kingdom Covenant is the covenant that enables the House of Judah to rule over the House of Israel according to the prophecy at Micah 5:2/Matthew 2:6.
COMMUNION AND THE NEW COVENANT
Christ introduced the New Covenant with the passing around of bread and wine and commanded that it be done "in remembrance" of him. Today we re-enact this occasion, calling it "Communion", "The Lord's Supper, or "The Lord's Table".
Luke 22: 19-20
Here, Christ is stating that the bread symbolized his body that he was about to sacrifice for us. This unleavened bread was to replace the Passover lamb, for under the Old Covenant, the Passover lamb symbolized Christ's body (this is discussed in detail under the page titled "The Lamb") (compare Exodus 12:1-11, with John 1:29, 1 Corinthians 5:7).
The entire nation of Israel was expected to eat of the Passover lamb under the Old Covenant, symbolizing the future expectation of Christ's sacrifice (Exodus 12:3-5). Likewise, the entire assembly of Christians is also to eat of the Communion supper because it signifies that Christ died for all, not just a few (2 Corinthians 5:14-15). The only real difference between the Passover of the Old Covenant and the Communion meal of the New Covenant is that the Passover was in expectation of his sacrifice (which was a future event at the time), and the New Covenant Communion is for the remembrance of that sacrifice now being past.
For some Christian groups, they believe Communion must include unleavened bread because "leaven" symbolizes sin and corruption (Matthew 16:6, 1 Corinthians 5:6-8), whereas Christ was to die without sin or corruption (1 Peter 2:21-22), and therefore was "unleavened". For other Christian groups, they accept leavened bread for the occasion because, since the bread symbolizes Christ's body (Luke 22:19), and Christ's body bore our sins at Calvary (1 Peter 2:24), they reason that using leavened bread is appropriate.
Next, Jesus took the cup of wine and passed that around the table, stating it symbolizes his blood that he was about to pour out for the cleansing of our sins. He specifically mentions that this is in relation to the New Covenant. Note that this includes, not just physical Israel today, but anyone who is of Spiritual Israel, for according to God all people can be cleansed of sin through Christ's blood. This is supported at Acts 10:28, 45, and Ephesians 3:6. Note that Christ stated that we were to "do this as a remembrance of" him, showing that this was to be a repeated occurrence on a regular basis until his return, as supported at 1 Corinthians 11:26.
According to prophecy, Jesus Christ is going to take some from spiritual Israel and make them the House of Judah to rule with him after his second coming.
It is evident in Scripture that the "Israel" of God is actually spritual Israel, not a group consisting of only the blood-related Israeli race. This "Spiritual Israel" is made up of all true believers in Christ regardless of national ties.
Also, the bread and the wine of the Communion supper are symbolic of Christ's sacrifice that cleanses all humanity from the curse of sin. This is the only way we can enter into the New Covenant, and have some chosen for the House of Judah.
Since all mankind is eligible to be covered under the New Covenant, then all who have true faith in this New Covenant are expected to share in eating the bread and drinking the wine.