What does [class] mean here, what does it do?

Question

.modal-popup .modal-slide {
    .modal-inner-wrap[class] {
        background-color: #f4f4f4;
    }
}

If I remove the [class] the styling doesn't apply, I'm guessing it applies the style to all the classes of the children elements.

Answer 1

Q: What does [class] mean here?

A: .modal-inner-wrap[class] will select all elements that have a CSS class modal-inner-wrap and that also have a class attribute (which they obviously have if they match the first condition).

Q: [...] and what does it do?

A: The only reason I can think of why one would add [class] is to raise specificity. This assumption is also supported by your observation

If I remove the [class] the styling doesn't apply