The words “fellowship” and “saints” are old-fashioned and rarely encountered in modern Evangelical/ Pentecostal circles.
JRR Tolkein’s first book in the Lord of the Rings trilogy is called “The Fellowship of the Ring”. Fellowship in that context, and generally, speaks of a group of people united in a common purpose. The purpose is greater than the individuals and calls for self-sacrifice and submission.
The word “saint” means sanctified one. In the context of Scripture, Paul writes to the saints at various places as members of the local churches there. Saints in the biblical context are those who have an ongoing, personal relationship with God in the context of the local church.
Put the two words “Fellowship” and “Saints” together and you have a group of people united in glorifying God through their lives together.