do this in remembrance of .... what?

1 Corinthians 11 

23For I received from the Lord what I also passed on to you: The Lord Jesus, on the night he was betrayed, took bread, 24and when he had given thanks, he broke it and said, "This is my body, which is for you; do this in remembrance of me." 25In the same way, after supper he took the cup, saying, "This cup is the new covenant in my blood; do this, whenever you drink it, in remembrance of me." 26For whenever you eat this bread and drink this cup, you proclaim the Lord's death until he comes.

we were to eat and drink the  Lord's Supper in remembrance of Jesus Christ.  ...all across the country, people are slowing down the service, perhaps dimming the lights, and playing some music while people stay in their seats and ... what?  what are they doing?  remembering what?  it is my experience that we are generally told to remember our sins.

but why then are people doing it in remembrance of their sins?  i suspect that it is because of a collective misunderstanding of the next couple verses...

 27Therefore, whoever eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of sinning against the body and blood of the Lord. 28A man ought to examine himself before he eats of the bread and drinks of the cup. 29For anyone who eats and drinks without recognizing the body of the Lord eats and drinks judgment on himself. 30That is why many among you are weak and sick, and a number of you have fallen asleep. 

while it certainly SEEMS to indicate we should examine our sins, this is not the context.  the context is that certain people were showing up with food - some ate all the food before others even arrived, some had plenty and ate all their food without offering it others who had nothing, some drank so much wine that they got drunk, etc.  some people would show up 'late' and other would show up so poor they had nothing, hoping to eat, and yet they left hungry.  how's that for fellowship and loving each other ?!
so, when these men were urged to 'examine himself', they were being urged to think about how much they were eating and drinking.  have they had enough to eat?  enough to drink?  do they have plenty and can give to others?  must they eat now?  or can they not wait to enjoy a meal with Christian brethren?

20When you come together, it is not the Lord's Supper you eat, 21for as you eat, each of you goes ahead without waiting for anybody else. One remains hungry, another gets drunk. 22Don't you have homes to eat and drink in? Or do you despise the church of God and humiliate those who have nothing? What shall I say to you? Shall I praise you for this? Certainly not!

...

29For anyone who eats and drinks without recognizing the body of the Lord eats and drinks judgment on himself. 30That is why many among you are weak and sick, and a number of you have fallen asleep. 31But if we judged ourselves, we would not come under judgment. 32When we are judged by the Lord, we are being disciplined so that we will not be condemned with the world.

 33So then, my brothers, when you come together to eat, wait for each other. 34If anyone is hungry, he should eat at home, so that when you meet together it may not result in judgment. 

      And when I come I will give further directions

indeed, it would be better to eat alone in their homes than to come to the gathering and eat everything up in front of people who had nothing.  ...if they would 'recognize the body of the lord' (that is, other Christians), then they would either share or, at a minimum, eat and drink alone at home.

[aside: i think all this may actually be related to the verse on the 'weak, sick and asleep'.  i suspect that some people could eat nothing and got weak. some others ate so much that they got sick, and still others drank so much wine that they fell asleep.  these are the consequences; and, though seemingly natural, they are described as 'the Lord's judgment'.  this is emphatically not punishment; Jesus Christ received all of the punishment in our stead.]

Takeaway
the Lord's supper is about remembering Jesus Christ, not about remembering your sins.
Application
it is suitable to remember Jesus Christ and rejoice in Him and in what He did at the Lord's supper; being dour and serious about your sins is not suitable at the Lord's supper.