Target elements with multiple classes, within one rule

• .border-blue.background { ... } is for when both classes are used together.

• .border-blue, .background { ... } is for either class.

• .border-blue .background { ... } is for where '.background' is the child of '.border-blue'.

See Chris' answer for a more thorough explanation. Also see W3 Docs on CSS Combinators

Just in case someone stumbles upon this like I did and doesn't realise, the two variations above are for different use cases.

The following:

.blue-border, .background {
    border: 1px solid #00f;
    background: #fff;
}

is for when you want to add styles to elements that have either the blue-border or background class, for example:

<div class="blue-border">Hello</div>
<div class="background">World</div>
<div class="blue-border background">!</div>

would all get a blue border and white background applied to them.

However, the accepted answer is different.

.blue-border.background {
    border: 1px solid #00f;
    background: #fff;
}

This applies the styles to elements that have both classes so in this example only the <div> with both classes should get the styles applied (in browsers that interpret the CSS properly):

<div class="blue-border">Hello</div>
<div class="background">World</div>
<div class="blue-border background">!</div>

So basically think of it like this, comma separating applies to elements with one class OR another class and dot separating applies to elements with one class AND another class.