In biology, dynamic equilibrium refers to a steady state of any biological element or system (such as a single cell, or an organ, for example) that has a higher level of energy than it's surroundings and thus requires work or activity to maintain.
The concept of dynamic equilibrium is very useful for understanding biological processes - especially at the chemical level of cells in aqueous solutions, considering all the movement of substances across their membranes both into and out of the cells.
To help conceptualize dynamic equilibrium, consider a swimming pool in the desert as an over-simplified representation of a single cell - it exists in an 'unnatural' state much different than it's surroundings would otherwise support. Left alone to the natural process of evaporation, the volume of water within this pool would decrease. But if a worker were introduced to the system, who constantly carried water from a distant oasis, and he added it to the swimming pool at the same rate water evaporated from it, a consistent volume could be maintained over time and the pool would achieve a state of dynamic equilibrium.
Perhaps the most straight-forward example of dynamic equilibrium in biology could be the steady internal body temperature of warm-blooded mammals. In order to maintain that temperature in the face of colder external temperatures, internal energy and activity are required, without which the animal's body temperature would otherwise come to equal it's external environmental one.