Talking about the rate order of a chemical reaction deals with the rate law for chemical reactions. The rate of a chemical reaction can be expressed in the generic equation below:
rate = k*[A]^x[B]^y
where [A] and [B] are the reactants of the chemical reaction expressed in units of concentration (moles per liter), k is the rate constant, and x and y are the exponents that are called the reaction orders of the individual reactants. If the exponent x is a 1, then the reaction is said to be first order with respect to the concentration of the reactant A. If the exponent x is a 2, then the reaction is said to be second order with respect to the concentration of the reactant B.
If a chemical reaction is dependent on two or more different reactants that can be very difficult to measure. One experimental way around this is to have an enormous excess of one of the reactants so that it's essentially constant and can be factored into the rate constant k. Then the reaction order of the other reactant species can be more easily measured. One example of this is the hydrolysis of an ester like ethyl acetate into ethanol and acetic acid.
CH3CO2Et + H2O --> CH3CO2H + EtOH
The rate of the above reaction is dependent on the concentrations of both ethyl acetate and water. If water is used as the solvent, then it is present in an enormous excess relative to the ethyl acetate and can therefore be considered to be constant through the course of the reaction, thus making it a pseudo first order reaction.