Why is Islam important for the Jews and Christians?

Just as it is important for you, it is important for them. Every other religion has expired so the only religion that is valid is Islam, as Allah Ta`ala says in the Quraan Shareef: إِنَّ الدِّينَ عِندَ اللَّهِ الْإِسْلَامُ. Further, Allah Ta`ala also states: وَمَن يَبْتَغِ غَيْرَ الْإِسْلَامِ دِينًا فَلَن يُقْبَلَ مِنْهُ - Whoever seeks a religion other than Islam, it will never be accepted from him.

And Allah Ta'ala (الله تعالى) knows best.