Dynamics are what actually happens when a game runs — the patterns of behaviour produced by mechanics interacting with player choices over time. Dynamics are not directly designed; they emerge from the mechanic definitions and cannot be fully predicted in advance (Hunicke, LeBlanc & Zubek 2004, see source-mda). A designer who wants a particular dynamic must engineer the mechanics that produce it.
Related: mda-framework, mechanics, aesthetics, emergence, systems-thinking, second-order-design