What does "communion of saints" mean in the Apostle's Creed? The original text can be found on wikipedia.

Near the end of the creed, there is this phrase:


  I believe in... the communion of saints...


What does this exactly mean? I understand that communion means a 'sharing in common', but I'm not entirely sure of the meaning and implications of this statement.

Note:

The Apostle's Creed is not unique to the Roman Catholic Church, and is accepted by many other denominations. I expect to hear the perspectives of all churches where the creed is accepted.
Wikipedia has a good article on the concept. The phrase means that Christians are united in the Body of Christ, a teaching based on 1 Corinthians 12 (and some other passages).