What Do The Lyrics 'Come Drink The Wine' Mean?

The lyrics 'come drink the wine' are used in reference to a part of the Eucharist. The wine refers to the blood of Christ. The Eucharist is an important Christian rite which is perform by priests in fulfilment of specific instructions left by Jesus Christ (noted in 1 Corinthians 11:24-25). These are instructions given by Christ which performed at his Last Supper to be done in his memory.  He takes the cup stating "This is my blood."

The bread and wine, over the course of this ritual are consecrated. Essentially once they are consecrated during the Eucharist, the Roman Catholic Church holds that they are no longer bread and wine, but rather, they turn into the body and blood (respectively) of Christ.