Go to one church, and it is open to all. Go to another, only for members. Still another, for believers in Jesus. This other one, it's for everyone. That one, only if a profession is made. It may be worth fighting over, as it is a serious thing, at least according to my belief. I probably couldn't be convinced that it's not also a serious thing in the bible. Which I also hold to being the infallible inspired word of God, usually seeking to be understood by fallible, hopefully inspired people like us. Several places have nice cards available for reading about what communion is, and whether one should partake or not.
A while back, I attempted to form some kind of belief about communion according to religion, and I believe it does hold some weight, and it also tracks fairly well. In evangelical churches, typically the words of Paul are used to institute communion, and often it is seen as a remembrance of Christ giving his body and blood. More traditional and Liturgical denominations seem to prefer the words of Jesus himself for the institution, and it is a sharing in his presence in whatever form along with the remembrance that is actualized in taking the elements.
Whether the memory of or the thanksgiving for, or the presence with, or to share fellowship with God and man, communion will always be an important part of our faith, as a real, tangible way we connect with the sacrifice Christ made on our behalf. That I believe is the point, and that is where those who are unsure may just want to further investigate before they partake, lest they forsake- Almighty God.