A dynamic simulation describes time-dependent behavior of a system. Therefore, the dynamic problem includes:
(1) non-linear algebraic equations (describing steady-state mass and energy balances, thermodynamic and kinetic equilibrium, or other phenomena), and
(2) ordinary differential equations (ODEs) that describe time dependent accumulation and disappearance of mass and energy, including the reaction kinetic terms.
All this should be standard material in your transport phenomena, unit operations, and reaction engineering courses.
It should be obvious that commercial simulators for dynamic simulation are far more complex than those solving pure steady-state problems. However, the generalized solution of large systems of differential equations is a highly non-trivial task, especially if some of the differential equations become "stiff" (i.e., when their time constants are small). I don't believe that the major commercially available chemical engineering dynamic simulators handle this aspect too well, as they do not incorporate the special numerical methods required for stiff ODEs.
Therefore, it is extremely important to validate the dynamic solution you get from ANY software package, a task that is neither easy nor quick.