We present a transparent conducting electrode composed of a periodic two-dimensional network of silver nanowires. Networks of Ag nanowires are made with wire diameters of 45-110 nm and a pitch of 500, 700, and 1000 nm. Anomalous optical transmission is observed, with an averaged transmission up to 91% for the best transmitting network and sheet resistances as low as 6.5 Ω/sq for the best conducting network. Our most dilute networks show lower sheet resistance and higher optical transmittance than an 80 nm thick layer of ITO sputtered on glass. By comparing measurements and simulations, we identify four distinct physical phenomena that govern the transmission of light through the networks: all related to the excitation of localized surface plasmons and surface plasmon polaritons on the wires. The insights given in this paper provide the key guidelines for designing high-transmittance and low-resistance nanowire electrodes for optoelectronic devices, including thin-film solar cells. For the latter, we discuss the general design principles to use the nanowire electrodes also as a light trapping scheme.