You ask a very widely defined question, so I am afraid an answer has to be very general.
A dynamic system is a system where things are not static, i.e. system response changes with respect to variables, e.g. time, environmental conditions and so on.
A dynamic model is one that tries to predict or post-process such changes. Predictive dynamic models assume relations and predict the input as function of varying variables, often described by an equation, e.g. a differential equation.
To validate a dynamic model one tends to vary its inputs and in controlled experiments measure the output. If the input-output is correctly descibed by a model, one may claim to have validated or Quality Assured the theory.
A predictive equation (theory) can be used also to break down a dynamic system into its typical bits and pieces. When we know how to do this, we can use response measurements to analyze data and try to identify dominant behaviors.
There are many techniques to do this and the applicability of any technique depends on your problem.
Here is a very good discussion on the Theory of Theory buidling
I see from your profile that you are into working with people which makes the above all the more difficult as you likely will have a ghost in the machine that makes identification of input-output relations all the more difficult. :)
I work with dead matter, i.e. things without a will of their own. If you are interested there are some ramblings of mine on the matter of analysis, measurement and Quality assurance written here. Part of this discussion is general and may be of use also for you. http://qringtech.com/learnmore/why-simulate-measure-correlate-automate/
Modeling dynamic has so many purposes. It is used in Aerospace Vehicle system, Public debt and economic growth system, Hydrodynamic system, business management system, quantum mechanics and so many other area .