Anyhow, back to my question, the answer to which I didn't fully understand. Can you send a unit to 'in between' area between two nodes? If so, then what purpose do nodes serve?
eadingas already answered the question for the most part. Dodging a single square object isn't very hard, but finding a way through a complex city is a whole other matter. That's what pathfinding routines are for - the CPU checks all possible routes to the destination and returns the most efficient one. A human would be able to guide their troops trough the streets, but the AI player would probably go insane. The node system splits the cities up in squares connected by straight lines.