Quadrature is in general a method for evaluating intergrals numerically which otherwise cannot be solved using elementary forms. In this case, single point quadrature is likely referring to a method whereby in each subinterval of the total interval over which the integral is defined, only one point of the integrand will be evaluated. But this is for each subinterval. Summing the subintervals (where for each subinterval we're computing its area numerically, i.e., the one point where the function gets evaluated (the height) times the width of the subinterval (the base)), we get an approximation of the total area, i.e., the value of the integral. The above is referring to the one dimensional case.
In this case, it appears one point quadrature may be referring to the midpoint rule.