When I typed [class] {background-color:crimson}, the whole page background becomes crimson.

It would be better for us if you could post the entire code, this way, we could spot the mistake easily !

Here is an exemple, I applied the crimson to a class as you suggested in the small exemple you typed.

http://codepen.io/Azuk/pen/asJfo

If you don't find the mistake, post your code :) !

Did you really typed... [class] ? If you typed that, then that is the reason why. Try using the class selector name instead. For example if the class has the value... customers... ie.

class = "customers" - select it this way

.customers{
background-color: crimson;
}

OP, you are correct. In the video for this tutorial Guil clearly types

[class] { background-color: crimson; }

And it does indeed target all anchors with a class attribute in them and make them Crimson. However when following this tutorial, my result is the same as yours.

I was following along via CodePen.

When I did this in Sublime Text 2, the class attribute works properly and targets every element on the page with a class attribute.

Perhaps it's a bug within CodePen?

I didn't see the code, but I'd check if the body element has a class attached