Not neglecting to meet together, as is the habit of some, but encouraging one another, and all the more as you see the Day drawing near. - Hebrews 10:25 (ESV)
Before explaining why we should tell you what is fellowship.
Fellowship is participation, sharing, and communion around the embrace of the gospel by the people of God.
Fellowship describes the unity and community of the church that can exist because of the gospel. As such, it is important to note that fellowship with other Christians can exist because God took initiative to bring us into right relationship with him. God the Father, through Jesus Christ and by the Spirit, has established, by his grace, a covenantal relationship with humanity. Those who believe the gospel are united in the Spirit through the Son to the Father (John 15:1–17; 17:1–26; 1 John 1:3–7). This relationship leads to the reality of communion between man and God. Those who are thus “in Christ” are in communion not only with Jesus Christ (and the Father) in the Spirit but also with one another. This relatedness, relationship, and communion is fellowship. Fellowship did not begin among humans, however; it stems from Trinitarian realities, namely the eternal fellowship of the three persons in the Triune Godhead.
Fellowship means that as a community of faith believers will commit to fulfilling the “one another” commands of the New Testament. Prescriptions from God, such as “love one another,” “forgive one another,” “pray for one another,” and “be devoted to one another,” are all meant to find their completion within the local church. This outworking of gospel truth within the lives of believers is a clear demonstration to the world of the church’s love for God and one another (John 13:35).