Initially process simulation was used to simulate steady state processes. Steady-state models perform a mass and energy balance of a steady state process (a process in an equilibrium state) independent of time. 
Dynamic simulation is an extension of steady-state process simulation whereby time-dependence is built into the models via derivative terms i.e. accumulation of mass and energy. The advent of dynamic simulation means that the time-dependent description, prediction and control of real processes in real time has become possible. This includes the description of starting up and shutting down a plant, changes of conditions during a reaction, holdups, thermal changes and more.
Dynamic simulation require increased calculation time and are mathematically more complex than a steady state simulation. It can be seen as a multiple repeated steady state simulation (based on a fixed time step) with constantly changing parameters.
Dynamic simulation can be used in both an online and offline fashion. The online case being model predictive control, where the real-time simulation results are used to predict the changes that would occur for a control input change, and the control parameters are optimised based on the results. Offline process simulation can be used in the design, troubleshooting and optimisation of process plant as well as the conduction of case studies to assess the impacts of process modifications. Dynamic simulation is also used for operator training.