The Greek ekkladō means to break off or snap off — specifically of branches broken from a tree. Paul uses this word exclusively in Romans 11:17-20, his extended metaphor of the olive tree. Some branches (unbelieving Israel) were 'broken off' (ekkladō) so that wild branches (Gentiles) could be grafted in. The same word appears three times in this passage.
Romans 11's olive tree imagery is a foundational NT text on election, Gentile inclusion, and Jewish hope. The natural branches (ekkladō) were broken off because of unbelief — not permanently, for Paul insists 'if they do not persist in unbelief, they will be grafted in again, for God is able to graft them in again' (v.23). The Gentile who stands proudly should fear: 'Do not be arrogant, but tremble. For if God did not spare the natural branches, he will not spare you either.' The entire passage calls for humility, awe, and hope in God's sovereign mercy.