A modeling framework for the internal conformational dynamics and external mechanical movement of single biological macromolecules in aqueous solution at constant temperature is developed. Both the internal dynamics and the external movement are stochastic; the former is represented by a master equation for a set of discrete states, and the latter is described by a continuous Smoluchowski equation. Combining these two equations into one yields a comprehensive theory for the Brownian dynamics and statistical thermodynamics of single macromolecules. This approach is shown to have wide applications. It is applied to protein-ligand dissociation under external force, unfolding of polyglobular proteins under extension, movement along linear tracks of motor proteins against load, and enzyme catalysis by single fluctuating proteins. As a generalization of the classic polymer theory, the dynamic equation is capable of characterizing a single macromolecule in aqueous solution, in probabilistic terms, (1) its thermodynamic equilibrium with fluctuations, (2) its transient relaxation kinetics, and most importantly and novel (3) its nonequilibriurn steady state with heat dissipation. A reversibility condition, which guarantees an equilibrium solution and its thermodynamic stability, is established, an H-theorem-like inequality for irreversibility is obtained, and a rule for thermodynamic consistency in chemically pumped nonequilibrium steady state is given.