Paul wrote that ancient Israel was like an olive tree stump, and the Gentile believers were like branches from wild olive trees that have been grafted into the 'root' of Israel.  Those Jews who rejected Jesus were like branches which were broken off from the original tree.  

Paul then appealed to Gentile believers not to be proud.  They were only grafted into the promise of Israel because of God's grace.  They have no right to think they are superior; they were not the reason the church existed; for Jesus Christ is the life of the church (John 15:1-5).  He is the original stump of the tree (Isaiah 11:1 and Isaiah 11:10).

The original 'branches' (Israelites who did not believe) were broken off because they refused to trust in Jesus Christ.  But that was no reason why Gentiles should look down on Jews; they were not in God's kingdom on their own merit but because of God's grace.  Applying the same reasoning, Paul says that the Gentile believers should be in awe of God, who has proved that He can and does remove 'unbelieving branches' (John 15:6).  The challenge was to stay true to the faith, keep receiving spiritual life from Jesus and stop being spiritually proud, or risk God's wrath.

Pride is the endemic disease of sinful humanity.  It is the pretence that we are better than others and have more value because of our work, wealth or status in society or the church.  But it is a lie.  The truth is that only God's grace can lift us out of our sin, and only His mercy can keep us away from His wrath. If the Apostle Paul should say, "For I know that good itself does not dwell in me, that is, in my sinful nature ..." (Romans 7:18) - then which of us has any reason to be proud?  But more than that, if God did not spare Israelites who disbelieved and refused to fully trust in Jesus, should we not take our faith much more seriously?  Unbelief is dangerous because it takes us outside of the blessing of God and exposes us to His wrath.  If that was true for the Jews who rejected Jesus, will it not also be true for us?