We investigate the mechanism of extraordinary optical transmission in subwavelength metal hole arrays. Experimental results for the arrays consisting of square or rectangular holes are well explained by the dependence of transmission strength on the polarization direction of the incident light. This polarization dependence occurs in each single hole. For a hole array, there is in addition an interplay between the adjacent holes which is caused by the transverse magnetic field of surface plasmon polaritons on the metal film surfaces. Based on the detailed study of a single-hole and two-hole structures, a simple method to calculate the total transmissivity of hole arrays is proposed.