A Dynasty is a collection of individuals belonging to a family group. They represent your family and workers. In most missions there are rival dynasties who are the main foil to your plans, the main targets for your nefarious deeds or, if you need help, they can become allies with enough toadying.
The main Dynastic opponents (as well as yourself) are represented by a simple coat-of-arms with a corresponding color. This color is shown as flags on buildings owned by your dynasty, as well as on your handcarts and the clothes of your employees.
In order for a Dynasty to survive there must be a married partner or offspring who has come of age (16 years old).