I have heard this statement many times, but I don't understand it. What does it mean exactly?
An interesting question!
I think it was Kramnik who, when asked who the best player on earth was, mentioned some other player. When asked why not Carlsen he replied: Magnus is from another planet!
That such a great player as Kramnik, conquereor of Kasparov, was in awe of Carlsen speaks volumes.
His "sight of the board" is phenomenal as is his ability to detect tactical possibilities.
How does he create opportunities for his opponents to go wrong?
The simple answer is by continuing to play!
He seems to absolutely love playing chess and plays out positions that many other GM's would pass up as too dry and drawish.
He has a superb ability to find resources in any position where other GM's cannot. Sometimes the advantages are only microscopic but Carlsen is willing to steadily seek out and accumulate these and convert drawish positions into winning ones.
Carlsen seems content to just get a playable position out of the opening rather than dominate with superior opening knowledge like Kasparov could do.
If you play through his games he often switches play back and forth from the centre then to one wing then to the other. He keeps sustained pressure on his opponent and squeezes as much as possible out of any position.