Communion, in simple terms, means intimate exchange, whether of ideas or emotions.
In Christianity, Holy Communion is the name of the service at which bread and wine are blessed and shared among congregants. The theological understanding of this ritual differs across denominations but it the general idea is that when a worshiper eats the bread and drinks the wine, she is assimilating the body and blood of Jesus into her own body and being.
The word 'symbol' does not quite capture the significance of this ritual, as the bread and wine do not simply 'stand for' the body and blood of Christ, but rather 'are' them.
The idea of communion can be extrapolated, though, from this ritual, to include ideas of assimilation and intimacy in a larger sense; the ways in which Christians are in communion with their church, for example, or with one another.
Ultimately, communion is a state of relationship to the world, one that people of any faith (or lack thereof) can hope for.