The purpose of replica-exchange molecular dynamics is to provide adequate sampling of a wide conformational space MD simulation.  In MD simulations, especially for biomolecules, the energy landscape often contains large energy barriers that will trap the system in saddle points, or local minima.  In order to find the absolute minimum of the system we require a method that will allow us to cross over the large energy barriers in search of deeper minima.  This is where replica-exchange helps us.  In replica-exchange we create several copies of a system that are identical except for their temperature.  The higher temperature replicas will be better able to sample over the entire conformational space and not be trapped as easily in local minima.  Each replica is searching for energy minima.  After a set number of steps in the simulation the energy of each replica is compared with its nearest neighbor(s).  Exchanges of temperature are then determined according to the following probability: min{1,exp(ΔH*Δβ).  Thus, if a higher temperature replica is at a lower energy than the lower temperature replica, the temperatures will be exchanged and the simulation continues.  If the energy is greater there is still a chance, although small, that the temperature will be exchanged.  The basic rundown is this: if a high temperature replica finds a deep energy well, the temperature will be lowered for the newly found well repeatedly until the absolute minimum is reached.  If an even deeper energy well in the landscape is discovered by a higher temperature replica, the process repeats itself focusing on the new energy well.  This continues until, ideally, the absolute minimum of the energy landscape is found.

References:

Sugita and Okamoto, Chem Phys Lett, 1999
Nymeyer et al, Methods Enzymol, 2004