It could be a number of things. Paul was known to simplify the deep things of the spirit into ways the everyday reader could understand. So the question then becomes what is an "unworthy manner," at least in regards to communion or the Lord's supper.
1.) Most I believe would say that it means, observing the Lord's supper without knowing Christ himself. I highly doubt that the apostles, especially the apostle Paul, would allow people who didn't have Christ dwelling within them take part in the communion meal.
2.) "This do in remembrance of me." The shere depth of what it means to drink Christ's blood and eat Christ's flesh has became a mere reflection of what it once was. The 11 were there, literally handed the cup from God himself in the flesh saying "Take this and drink, this is my covenant (promise) to you." Which at that time was more or less a marriage proposal in Hebrew custom. That though is a discussion for another day but if interested look up passages about the Church being referred to as the "Bride of Christ."... Point being, if you were going to share in eating the flesh and drinking the blood you were not to do so with unrepented sin, or more importantly a dead spirit. To take part in the communion without being a born again follower of Christ was and is basically slapping Christ in the face and casting down the price He paid on the cross when He shed His blood, and allowed His body to be broken for our sakes.
Other.) Any other issues that could be reffered to as "unworthy" would essentially point back to these, or could the endless debates over the more minor details of the Communion such as: wine vs. juice, time of day, the day in which to take part in the meal, what kind of bread, and various other things.
I hope this helped you.