fellowship meal

What is fellowship? The Webster dictionary says its:A friendly relationship;the condition or fact of having common interest,ideals, or experiences.
But what exactly does the word fellowship mean in a religious context? When I think of fellowship I think of a group of people getting together for a meal and/or discussion and friendly conversation.
The apostles and followers of the new christian faith started out their Sabbath by going to Temple then going to homes or catacombs for prayer,communion and fellowship.
If this is what fellowship is then how do we get people who are not yet religious or faithful to join us in a common meal and friendship? Does this word frighten people away by thinking we're dragging them into a prayer group?
Several weeks ago my husband and I,along with Fr.Peter and John,attended a free meal at St.Hedwig,in Southbridge mass,the meal was set up to help feed the community in town.While talking to one of the organizers he said that allot of the people attending their meals we mainly elderly church members,from their church, and he was not sure if this was because they called the meal a fellowship meal, maybe the people from the community may have been frightened off thinking this may be a conversion/prayer type thing and not just a free meal.
To tell you the truth I never thought about this but after he said that it made me wonder if this was true.I'm not sure if I was a person of no particular faith if I would feel there was some ulterior motives on the part of the church.It just brings to mind though that when we decide to do things in the community we need to be sensitive to the words we choose,the same word can have different meanings for each one of us depending on where we stand.What might be a simple act of caring and friendship form one person perspective may seem frightening to another person.