There are many cities on this planet we call earth and there is one thing true of them all. None of them will last forever at least as we know them today. “For here we have no continuing city, but we seek the one to come” (Heb.13:14). In the context the writer of Hebrews is specifically referencing the temporal nature of the city of Jerusalem. It like the Old Covenant it represents will also pass away. Those who have entered into the benefits of the New Covenant through faith in Jesus Christ, Who died for their sins and rose again, look for the city that is to come. That city is none other than the New Jerusalem which God has prepared for them (11:16). That heavenly city will one day be inhabited by God and His people on the new earth (Rev.21:1-3).
For the original recipients, Jewish people who had professed faith in Christ, this verse (13:14) was meant to motivate them to continue following Jesus as they looked for the New Jerusalem where they would dwell with Him forever. They were not to go back to the Old Covenant represented by the earthly city of Jerusalem. We too, as we look for new heavens and new earth on which the New Jerusalem will be situated should be motivated to live holy and godly lives (see 2Pet. 3:10-18).