It was ordained for the continual remembrance of the sacrifice of the death of Christ, and of the benefits which we thereby receive. The bread which in the Lord's Supper is broken, given, and eaten, is meant to remind us of Christ's body given on the cross for our sins. The wine which is poured out and received, is meant to remind us of Christ's blood shed on the cross for our sins. He that eats that bread and drinks that wine is reminded, in the most striking and forcible manner, of the benefits Christ has obtained for his soul, and of the death of Christ as the hinge and turning point on which all those benefits depend.
Now, is the view here stated the doctrine of the New Testament? If it is not, forever let it be rejected, cast aside, and refused by men. If it is, let us never be ashamed to hold it close, profess our belief in it, pin our faith on it, and steadfastly refuse to hold any other view, no matter who teaches it. In subjects like this we must call no man master. It matters little what great theologians and learned preachers have thought fit to put forth about the Lord's Supper. If they teach more than the Word of God contains they are not to be believed. Taken in part from J.C. Ryle's book The Lord's Supper.
Other parts of his letter:
Why was the Lord’s Supper ordained?
Who ought to receive the Lord’s Supper?
What benefits are in receiving the Lord’s Table
What effects are in receiving the Lord’s Table
Warnings concerning the Lord’s Table