It selects elements with the class `class` that also have the class `class`. The example might be a little abstract but it could be something like `.message.highlight`, which selects all elements with the class `message` that also have the class `highlight`.
Classes are for classification, IDs are identification. For styling you almost never need identifiers because that is not what styling is about.
<div class="message highlight">
.message.highlight {}
is much better than <div id="highlightMessage">
#highlightMessage {}
IDs are like singletons: not reusable.