From International Standard Bible Encyclopedia:

The Name and the Thing:

The name Agape or "love-feast," as an expression denoting the brotherly common meals of the early church, though of constant use and in the post-canonical literature from the time of Ignatius onward, is found in the New Testament only in Jude 1:12 and in 2 Peter 2:13 according to a very doubtful reading. For the existence of the Christian common meal, however, we have abundant New Testament evidence. The"breaking of bread" practiced by the primitive community in Jerusalem according to Acts 2:42, Acts 2:46 must certainly be interpreted in the light of Pauline usage (1 Corinthians 10:16; 1 Corinthians 11:24) as referring to the ceremonial act of the Lord's Supper. But the added clause in Acts 2:46, "they took their food with gladness and singleness of heart," implies that a social meal was connected in some way with this ceremonial act. Paul's references to the abuses that had sprung up in the Corinthian church at the meetings for the observance of the Lord's Supper (1 Corinthians 11:20-22, 1 Corinthians 11:33-34) make it evident that in Corinth as in Jerusalem the celebration of the rite was associated with participation in a meal of a more general character. And in one of the "we" sections of Acts (Acts 20:11) where Luke is giving personal testimony as to the manner in which the Lord's Supper was observed by Paul in a church of his own founding, we find the breaking of bread associated with and yet distinguished from an eating of food, in a manner which makes it natural to conclude that in Troas, as in Jerusalem and Corinth, Christians when they met together on the first day of the week were accustomed to partake of a common meal. The fact that the name Agape or love-feast used in Jude 1:12 (Revised Version) is found early in the 2nd century and often afterward as a technical expression for the religious common meals of the church puts the meaning of Jude's reference beyond doubt.

Origin of the Agape:

So far as the Jerusalem community was concerned, the common meal appears to have sprung out of the koinonia or communion that characterized the first days of the Christian church (compare Acts 1:14; Acts 2:1 etc.). The religious meals familiar to Jews--the Passover being the great type--would make it natural In Jerusalem to give expression by means of table fellowship to the sense of brotherhood, and the community of goods practiced by the infant church (Acts 2:44; Acts 4:32) would readily take the particular form of a common table at which the wants of the poor were supplied out of the abundance of the rich (Acts 6:1 ff.). The presence of the Agape in the Greek church of Corinth was no doubt due to the initiative of Paul, who would hand on the observances associated with the Lord's Supper just as he had received them from the earlier disciples; but participation in a social meal would commend itself very easily to men familiar with the common meals that formed a regular part of the procedure at meetings of those religious clubs and associations which were so numerous at that time throughout the Greek-Roman world.

Relation to the Eucharist:

From Glossary of Eastern Orthodox Terms:

Christian love, "charity" (1 Cor. 13:1-8). Saint Ignatius of Antioch and Saint Hippolytus of Tome (second century) use Eucharist and Agape as synonyms (cf.1 Cor.11); in Jude 12, the ‘love feasts’ are most naturally understood to be the combined Agape-Eucharists. The Agape (in Didache, 70-110) is a Jewish meal (Chaburah) Christianized as in the ‘new meal’ of Christ’s Kingdom and Love. Today the term Agape refers to the Easter Sunday’s Vespers (held either in the morning or the afternoon) which is also called the Second Resurrection Service. During this Service the Gospel reading relating to the first appearance of the Resurrected Christ to His disciples is read in many languages besides Greek, in order to emphasize the universality of salvation in the Resurrected Christ and its message to all people and nations.

From Zohiates, Word Study Dictionary of the New Testament: Word: Plural, aGApai