We investigate the time-reversal symmetry of nonequilibrium fluctuations. Their dynamical randomness can be characterized in terms of the standard and time-reversal entropies per unit time of dynamical systems theory. In particular, we present experimental results for a Brownian particle in a moving trap, showing that their difference equals the thermodynamic entropy production. This shows that the thermodynamic entropy production finds its origin in the time asymmetry of the dynamical randomness. Such concepts also give new insights to the physics of information, such as Landauer's principle.