First off, I want to say that it's all relative. somewhat...
Here's a good illustration that I've stole from Movie Bear
Now, projected white on a grey screen will never be white. It will always be gray. But your perception can make you think it's white if no other references are present.
So what does a grey screen actually do? Although is does lower the floor for black it also lowers the ceiling for whites too....and of course everything in between. So are colors accurate? NO. Some say they become overly saturated. I think this is a misuse of the term saturated as I prefer to think they have taken on a darker hue of the original color.
What's the most accruate coloration? a white screen.
Then how can some find Grey screens benefitial? Because it's all about perception. If all you have in the room is a grey screen your whites will likely look white to you.
If you've done many side by side comparisons though, you start to formulate a reference memory. Then when you look at a grey screen all you can think of is why the colors and whites look off. Fortunately humans have short memories so I think this eventually adjusts to think everything is accurate again. I'm only a month into the test driving of a grey screen and I still can't shake it, but I'm trying...
It essentially becomes a personal preferance. I personally like white screens. I'm not willing to compromise my whites and colors just to get slightly darker blacks.
Grey screens became popular because of the diffeciency of digital projectors with blacks. So, with digital projectors getting better are grey screens gonna go bye bye? Yes and No. Grey screens can help when you can't control the lighting in your room. The blacks on your screen can only be as black as the screen when no light is projected on it. So, starting with a screen that is already darker(grey screen) gets you that much closer to a satisfying black level for your ambient light conditions. Generally if you have control over your ambient light, and you have a decent CR projector, you don't need a grey screen.
Here's a good color information link I've used in the past