Like commas, the "long" or "em" dash is used to break up the content of a sentence into sub-clauses. Sometimes this is used to add ancillary information -- information which is useful but not necessary to the sentence.
Without these sub-clauses the sentence would simply read:
Her architectural wonders cause the people in the dream to search for the intruder, like white blood cells drawn to a virus.
The first sub-clause, "projections of Cobb's subconscious", gives us more information on who the "people in the dream" are. The second sub-clause, "Ariadne", tells us the name of the "intruder". Neither is required to understand the sentence, but may still be useful information.