Dynamic analysis means figuring out how the value of a variable changes over time.
There are two kinds of dynamics: equilibrium dynamics and disequilibrium dynamics.
In growth models we analyze how the equilibrium value of a variable such as GDP per worker moves over time. This would be an equilibrium dynamics. In disequilibrium dynamics we analyze how the value of a variable moves from one equilibrium value to another. This is also called transitional dynamics. Suppose for example the equilibrium price of a good is $10. If consumer income increases, the equilibrium price will increase to $15 due to an increase in demand. During the time the price is increasing from $10 to $15, the market is in disequilibrium. In fact the reason for the price change is market disequilibrium. The disequilibrium dynamics analyzes the path the price travels going from $10 to $15. It is also called transitional dynamics because the market is transitioning from one equilibrium to another.