The term κοινωνία, G3126, usually means “fellowship” or “communion.” It also means “a sharing.” Paul employs it for the offering which the Gentile churches were giving “for the poor among the saints at Jerusalem” (Rom 15:26).
It would seem that after the Day of Pentecost (Acts 2) a considerable number of the new converts may have remained in Jerusalem, to enjoy the Christian fellowship of the believers there. Probably also widows (cf. Acts 6:1) and other poorer Jews were cut off the relief rolls when they became Christians. Even a partial community of goods (Acts 2:44, 45; 4:34, 35) did not prove adequate. The church at Antioch once sent a famine relief offering to Jerusalem (Acts 11:27-30).
Paul wrote to the Corinthians twice about the matter of their taking up an offering for the Jerusalem saints. He requested that they give weekly, in proportion to their income (1 Cor 16:1-4). Representatives of the church would accompany the contribution as also from the churches of Macedonia, Asia, and Galatia (Acts 20:4). Paul urged the Christians at Corinth to make sure that their giving matched their enthusiastic pledging (2 Cor 9:1-5).
When Paul left Corinth on his third journey he hoped to go to Rome, but he felt constrained to accompany the contribution to Jerusalem (Rom 15:22-29).
R. N. Longenecker, Paul, Apostle of Liberty (1964), 227-229.
International Standard Bible Encyclopedia (1915)