Although Christians often speculate about various meanings of the Lord's Supper, the basics are beautifully stated in the following two collects.
Almighty Father, whose dear Son, on the night before he suffered, did institute the Sacrament of his Body and Blood; Mercifully grant that we may thankfully receive the same in remembrance of him, who in these holy mysteries giveth us a pledge of life eternal; the same thy Son Jesus Christ our Lord, who now liveth and reigneth with thee and the Holy Spirit ever, one God, world without end. Amen. (1928 BCP, p.152)
Grant, O Father, that when we receive the blessed
Sacrament of the Body and Blood of Christ, coming
to those holy mysteries in faith, and love, and true repentance,
we may receive remission of our sins, and be filled with thy grace and heavenly benediction; through
Jesus Christ our Lord. Amen. (1928 BCP, Offices of Instruction, p. 295)
Thanks be to God for this great and holy gift!