A complex media query is one where the browser looks at multiple conditions to asses when the rules should be applied. This could also be known as a multi-part conditional statement.
For example, we might have a media query that looks to be larger than some size, but also smaller than another size. We could write this like;
@media (min-width: 500px) and (max-width: 600px) {
/* Do Something */
}
You can read more about media queries on the Mozilla Developer Networks site;