I don't know what it "means to Christians," but Disciples of Christ (Gospel of Christ believers), were "commanded" to "... this do in remembrance of me." (I Corinthians 11:24) We should always "remember" that the shedding of "His blood" is what affords us the opportunity to "eternal life!"
However, do we "remember Him" by taking what He told us to take (bread and water) for the Communion? Most take "wine" for Communion although Scripture tells us in Romans 14:13-23 but v21 in particular which says "It is good neither to eat meat NOR TO DRINK WINE, nor ANYTHING by which thy brother stumbleth or is offended, or is made weak." Do you think He wants us to take ANYTHING (Wine) that causes "thy brother to stumble" for Communion? "Religion" errs according to Scripture!
What about "grape juice?" Matthew 26:29 and Mark 14:25 does say "...I will not drink henceforth of this "fruit of the VINE..." which is an allegory! John 15:1-10 says (v1) "I AM THE TRUE VINE..." which proves that the "VINE" is an "allegory" of how Jesus is the VINE and we should be "branches of Jesus" (Christ-like) which has NOTHING to do with what is "in the cup" for Communion!
Everything and I mean EVERYTHING one should do for salvation is written in the Word of God! What should be "in the cup" for Communion is given us in Scripture and can be found if His Word is "rightly divided" praying and seeking guidance from the Holy Spirit!
Did not Jesus say in Matthew 26:28, Luke 22:20 and I Corinthians 11:25 that the "new testament" (or New Covenant) was "IN HIS BLOOD" which was "SHED?"
Did not John 19:34 tell us that "...one of the soldiers, with a spear, pierced his side, and immediately came there out blood and WATER?" Do you notice the importance of the next verse (v35)? "WITNESS...that you might "believe!"
Well, there, now you have it! TRUTH! What "religion" does NOT teach!