The very first word in 1 Cor. 11:23, for, alerts us that Paul is about to give the reason why the exposed problem in vv.17-22 is so serious.  It’s because of instruction that originated from the Lord Jesus himself, as is clearly captured in the Upper Room narrative found in the Synoptic gospels.  It is called the Lord’s supper after all, which in this case means that the Supper is not only about the Lord, but also comes from the Lord.
So unsurprisingly, Paul’s instruction he received from the Lord lines up with what we read in the gospels, most closely with Luke’s account.  The bread signifies Christ’s body handed over to be crushed, whereas the cup represents the blood shed for the establishment of the new covenant, which includes the forgiveness of the sins of all who are included it in.  What clearly stands out is the repetition of the phrase: in remembrance of me.  While this statement by Christ is found in Luke’s account, it does not appear in the other gospels.  So the question becomes:
Why is it emphasized here in 1st Cor. 11?  It’s hard to say for certain, but perhaps they had already started to get confused about the meaning of the ordinance.  Regardless, Paul wanted to take time to remind them what the Lord’s Supper was pointing to, namely the very foundation of their lives; the Lord of glory coming to give his life as a ransom payment for sinners!
However, look at v.26, which contains content that does not appear explicitly in the gospels.  When the church conducts this ordinance, it serves as a proclamation of the gospel throughout the church age.  Along with the preaching of the message, the practice of the ordinance of the Lord’s supper announces to everyone Christ’s death on the cross.  No wonder the Corinthian church and all churches need to handle this practice with extreme care since a perversion of the practice of the Lord’s supper leads to a perversion of the presentation of the death of Christ!