James, Peter and John, those reputed to be pillars, gave me and Barnabas the right hand of fellowship when they recognized the grace given to me.The "Right Hand of Fellowship" doesn't just mean that the other apostles shook Paul's hand. In Christian tradition, this indicates a full acceptance and endorsement of Paul's message. Essentially, a public announcement to anyone looking on "this guy is not only our friend, but our brother and fellow worker in Christ".
Galatians 2:9a
Even today, many Christian denominations (though not the EFCA) takes part in the "right hand of fellowship" as part of their church services. A new attender or prospective member is examined by the pastor or elders. Then, if they are shown to be upright people and devout followers of Christ, they are "extended the right hand of fellowship" and asked to shake the right hand of everyone in the Congregation. This informs everyone in the Congregation and everyone from the outside that this new person has been accepted as a full brother or sister of the church.