What is raid clutter? Well, it's that mess of stuff that goes on during a raid encounter. It can be a boss, it can be trash, that's not really important. What is important is that absolute mess of spells going off, that can make it almost impossible for you to see anything. As fights get more complex with more encounter mechanics that need to be observed and reacted to, the clutter of modern raiding becomes more and more difficult to deal with. To use one example, the Dark Shaman fight is an absolute bonanza of raid clutter, especially on heroic - even separating the two shaman only means that half the raid gets to deal with tombs falling from the sky and ground effect cones while the other half of the raid has big red circles and purple cyclones. And that's just the boss mechanics - it doesn't take into account every member of the raid casting some form of spell or using some attack or ability, most of which have a visual component.
But don't take my word for it. Blizzard knows this is a problem.