This is a guess but it probably refers to the theory of Communion; whether the eating of Christ's body and blood in the form of wine and bread is real or if it is a symbol to remember Christ's sacrifice by.
Consubstantiation is the Lutheran terminology to describe their theological understanding of Holy Communion. This includes belief in what they term the 'real presence' of the body and blood of Christ as being 'in, with and under' the existing physical elements of the bread and wine. The Latin prefix 'con' means 'with' in English, hence the term 'consubstantiation.'
Memorialism on the other hand is the belief taught in a number of churches, including Baptist and Reformed that the meal which Jesus taught Christians to observe is a memorial meal and does not involve any actual or real presence of the body and blood of Jesus. They believe it is intended to act as a memorial or solemn remembrance of the suffering and death of Jesus on the cross of Calvary.
The one major difference is thus around whether or not there is actually the body and blood of Jesus Christ present. The Lutheran teaching is thus similar to both the Catholic and Anglican teaching here and differs from other denominations who hold it is a memorial only with no actual body and blood being present.
Consubstantiation
Catholic Church
The theological differences between different denominations is great... the meaning probably can be said to be the same. The Eucharist is believed to be the Body of Christ. Theologically the means whereby this comes about is: Catholics believe in transubstantiation Lutherans: consubstantiation Episcopals "transignification"; Calvin... a mystery. For all: "The Body of Christ"
Transubstantiation--The bread and wine of the Holy Sacrament become the Body, Blood, Soul, and Divinity of Our Lord and Savior Jesus Christ. Only the accidents of bread and wine remain. Consubstantiation--An error which maintains that the Savior unites Himself for a short period of time to the bread and wine which remain fully and completely bread and wine.
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