A zero means that the concentration for that reactant has no bearing on the rate of reaction. A one means that increasing the concentration of this reactant will increase the rate of the reaction in a linear way (doubling the reactant doubles the rate). A two means that the rate of the reaction will increase by the square of the increased concentration (doubling the reactant will increase the rate by four times). Zero order reactants are often not listed in the rate equation, since any number to the zeroth power is equal to one.
For example, if reactant one is first order (an exponent of 1) and reactant two is first order (an exponent of 1) then the overall reaction would be a second order reaction.
