Once you've taken control of a city, you can assign assassins to work in that city from the Guild interface. At the start, you can only assign 2 assassins per city, but building additional dens means you can assign additional assassins, up to a max of 5.
When assigned to work in a city, the assassins will generate income for you and help you to retain control of the city. The more experienced the assassins are, the better the job they will do. You can also assign these assassins contracts from the city they are currently responsible for.
Assigning assassins to a city removes them from your "normal" assassin roster - they will be unavailable to call in combat or send on contracts outside of their city. However, you will also be able to recruit new assassins to replace them. Do note that once you've assigned at least one assassin to a city, you can't empty the city completely out - you can swap assassins around, but once there's at least one in the city, there must always be one left.
I personally never used this mechanic, (I managed just a core team of "global" assassins who I could send on contracts and call in battle) and I found that I still had plenty of money and resources. If you find this particular aspect of the game interesting, though, then building additional dens is an important part of expanding your ability to utilize it.