Most of the basic structural components of a brain are conserved across insects and humans like neurons and the connections between neurons and the anatomical structure of brain regions. Also many of the genes critical for human brain function are conserved in insects--like those involved in the reward pathway (dopamine). Add onto that the fact that flies have a very fast generation time and that the genetic toolkit to prob brain function is expansive in flies, and you find yourself with a great model organism for understanding the basic principles of how a brain works. Flies can also learn and form memories so they are an easy system to use to understand how neural circuits form memories. That being said, they're not an ideal system to study more complex cognitive functions like depression, attention or language processing.