I read online that right now Ivanchuck is performing over 3150 in his currant tournament.  What does that mean?

It means he's playing extremely well.

lanceuppercut_239 wrote: It means he's playing extremely well.

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Well I figured as much, but how do they calculate it and how does it affect his actual rating?

It is a "performance rating". A hypothetical rating that is calculated from the games of a single event only. To do this, you take the rating of each player beaten and add 400, the rating of each player lost to and subtract 400, the rating of each player drawn, and sum these figures and divide by the number of games played.

An equivalent, and perhaps simpler arithmetically, formula is to take the number of wins minus the number of losses times 400 plus the average opponent rating (for all games including draws).

(W-L)*400 + Average_opponent_rating 

Or to put it in words, it means that Ivanchuk is peforming as well as a player with a rating of 3150 would be expected to perform. ie, he is performing very well

To me, performing at a particular rating means that you are playing at a level that is very different from your actual rating. Someone performing extremely well may play a few hundred points over their actual rating and someone performing extremely poorly may play a few hundred points below their actual rating. This happens to everyone at least once where they go through a period of extremely good or bad play but it usually evens out eventually. I find that for a short time after studying Bobby Fischer's games I play around 200 points higher than my norm but it usually doesn't last unless I keep refreshing what I learned.