No passage in the whole New Testament is of greater importance than this one (there may be others as important but I submit none of greater importance). It gives us our most sacred act of worship. If you have not read it, I encourage you to do so now.
What does the Last Supper mean? I do not think it was a spiritual accident that the meal in this passage occurred on Passover - in fact Jesus and His disciples were celebrating the Passover meal. Passover celebrated the deliverance of the Hebrews from slavery in Egypt. Holy Communion celebrates our deliverance from sin by Christ's death on the cross.
I also find a very spiritual meaning when Jesus tells His disciples, and us, to eat the bread and drink the wine in "remembrance of me". I wonder how many of us, and certainly me included, really dwell on these words. These words are extremely important to Holy Communion. Jesus is telling us to think, meditate, and pray about what He did for us and why He did it. When Holy Communion becomes just a ritual, and we do not concentrate on what Jesus did for us, it loses its significance. If we find this happening to ourselves, let's commit that we will return to this passage of scripture so we can be reminded of the significance of this act of our worship.
Paul reinforces this message when he says that no one should take Holy Communion in an unworthy manner. In reality no one is worthy to take Holy Communion. We are all sinners saved by grace. This is why we are called to prepare ourselves for Holy Communion through healthy introspection, confessing our sin, and resolving to live a new and better life. If we do this, the meaning of Holy Communion is properly defined in our minds, we become worthy to receive it, and we focus our minds on living a better life.
Wishing you much success in your walk with Christ,