Reaction intermediates are chemical species, often unstable and short-lived (however sometimes can be isolated), which are not reactants or products of the overall chemical reaction, but are temporary products and/or reactants in the mechanism's reaction steps.  Reaction intermediates are often free radicals or ions.
The kinetics (relative rates of the reaction steps and the rate equation for the overall reaction) are explained in terms of the energy needed for the conversion of the reactants to the proposed transition states (molecular states that correspond to maxima on the reaction coordinates, and to saddle points on the  potential energy surface for the reaction).