.class.class can also be used to avoid the use of !important in case that a higher specificity selector prevents your rule from being applied.
In this case there are not two classes in the HTML element. You only repeat the class which specificity you want to increase in the style (selector), like
<div class="class1 class2">
Hi I am ".class1.class2" selector
</div>
<div class="class1">
<p class="class2">
Hi I am ".class1 .class2" selector
</p>
</div>