Double dissociations in aphasia refer to a neuropsychological phenomenon where two related cognitive functions are shown to operate independently of one another, typically observed in patients with different types of language impairments. This concept helps researchers understand the organization of language processing in the brain by demonstrating how damage to specific areas can lead to distinct patterns of language deficits. By studying individuals with different forms of aphasia, insights are gained into the relationship between brain structure and function regarding language processing.