What does Hebrews 6:4-8 mean, and why does it say it is 'impossible' to be restored?

It means impossible; it is the ordinary Greek word for impossible. You have to look at the context: these are Hebrew Jews who converted to Christianity and are now hearing about the terrible persecution the Roman emperors are inflicting on Christians, while the Jews had a temporary reprieve. So they are tempted to go back to Judaism to save their skins. Paul, who I believe wrote Hebrews, tells them that after they have tasted the heavenly gift and shared in the Holy Spirit, to go back to Judaism is to repudiate Jesus Christ, and then it is impossible for them to return. It is very close to blasphemy; once you throw Jesus under the bus like that, you will never have the inclination to come back, so in that sense it is impossible. The same theme appears in Hebrews 10:26-31, where the one who leaves and thinks he can still be saved in Judaism receives a greater damnation, and it is a fearful thing to fall into the hands of the living God. This follows the New Testament's constant theme: endure to the end, no excuses. And in fact those who leave as convinced adults never do come back.