A pseudo first order reaction is a reaction that is truly second order but can be approximated to be first order under special circumstances.  For example, a second order reaction of the type A + B --> C is dependant on the concentrations of both A and B.  But monitoring the concentration of two different reactants at the same time is very difficult.  If one of the reactants is used in a very large excess then that concentration would hardly change at all and could be considered to be essentially a constant.  If [B]>>>[A], then the [B] would be essentially unchanged and the reaction could be considered pseudo first order with respect to [A] as a mathematical simplification.  An example of this is the hydrolysis of an ester to a carboxylic acid using water.  The reaction is truly second order and the rate depends on the concentration of the ester and water used.  But since water is often used as a solvent, then its concentration is in a huge excess compared to the ester and can be considered a constant.  Thus the reaction is pseudo first order for the ester.

What is a Pseudo First order reaction? Give one example.

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.