Why did the believers in Antioch rejoice when they read the letter from the Jerusalem Council?
They rejoiced because the letter brought consolation: Gentile believers were not required to keep the Judaic Law or submit to circumcision. The Jerusalem Council affirmed that no greater burden should be laid on them than necessary things, so they were free from all that.
Les explains that after the Jerusalem Council dismissed them, the messengers returned to Antioch, gathered the multitude, and delivered the epistle. When the believers read it, they rejoiced for the consolation that they did not have to keep the Judaic Law or circumcision; they were free from all that. The council had said it seemed good to the Holy Spirit to lay upon them no greater burden than these necessary things. They also had full permission to go and preach the Gospel of Grace to the Gentiles without being proselytized into Judaism. Judas and Silas, being prophets themselves, exhorted the brethren, and Silas remained there.