A Covenant Relationship
God has always had a special relationship with man. When He created Adam as the first human, the creation account records that God breathed life into him making him a living soul. Having a soul distinguished Adam from all the other animals that God created.
Because of this special relationship, God would make covenants with man. Covenants are basically promises and usually have conditions associated with the promise. Most often when God made a covenant with man, He asked for man to be obedient to His will. In some cases God made a covenant without any requirements from mankind, as He did with Noah and the promise to never completely flood the earth again.
Israel became a covenant nation because of a promise God made to Abraham. As a covenant nation they were required to live under the Law of Moses. This was not a choice the Israelites were given, where some could be a part of the promise and others would not. All were participants in this covenant as inherited from Abraham.
A Better Promise
God designed the first covenant with Israel for a temporary purpose - to prepare a way for Jesus to come and establish a second and better covenant for mankind. The new covenant offers great benefit to those who would be participants in it. For example, the forgiveness of sins and the hope of eternal life are both a part of the new covenant. Neither were a part of the first covenant.
Unlike the old covenant, the new promise is a promise of choice that has been extended to all nationalities and races. One is not born by birthright into the new covenant automatically, but rather chooses to become a part by accepting the terms and conditions it established.