The theory was that foods which contain cholesterol, such as eggs, would cause high cholesterol in people. There is a certain logic in that I suppose, but it has turned out not to be correct.
As is so often the case it is more complicated than that*. Cholesterol is essential and is manufactured by our bodies whether we eat any or not. Excessively high cholesterol levels are thought to be caused by saturated or trans fats. But not everyone believes that either!! Why some people have high cholesterol and some don't is not always due to their fat intake. It's a bit of a mystery!
All this has been known for quite some time, but the egg yolk myth has been very difficult to eradicate. I remember the look on my friend's face when he was describing the egg white omelette he was given in California a few years ago!!
(*I can't remember the name, but there is a science writer who was using the phrase "actually it's a bit more complicated than that" so often that he had it printed on a tshirt!)