You would use "class" to refer back a predefined CSS style. You can leave it out and the default or global styles will take place or you can specify a class and have those styles applied. This is great when you have multiple styles for one type of element and you want them to have different styles from each other.
Consider this CSS style:
Now, let's say you have a hyperlink on your website. Any hyperlinks you want to be red you would do this:
And any hyperlink you wanted blue you would do this:
You can do this with just about any element, not just anchor tags.