We present and use new spectra and narrow-band images, along with previously published broad-band images, of stars in the Arches cluster to extract photometry, astrometry, equivalent width, and velocity information. The data are interpreted with a wind/atmosphere code to determine stellar temperatures, luminosities, mass-loss rates, and abundances. We have doubled the number of known emission-line stars, and we have also made the first spectroscopic identification of the main sequence for any population in the Galactic Center. We conclude that the most massive stars are bona-fide Wolf-Rayet (WR) stars and are some of the most massive stars known, having \Minit >100 \Msun, and prodigious winds, \Mdot >10-5 \Msunyr, that are enriched with helium and nitrogen; with these identifications, the Arches cluster contains about 5% of all known WR stars in the Galaxy. We find an upper limit to the velocity dispersion of 22 km/sec , implying an upper limit to the cluster mass of 7(104) \Msun within a radius of 0.23 pc; we also estimate the bulk heliocentric velocity of the cluster to be v_cluster,o +95 km/sec . Taken together, these results suggest that the Arches cluster was formed in a short, but massive, burst of star formation about 2.5+/-0.5 \Myr ago, from a molecular cloud which is no longer present. The cluster happens to be approaching and ionizing the surface of a background molecular cloud, thus producing the Thermal Arched Filaments. We estimate that the cluster produces 4(1051) ionizing photons s-1, more than enough to account for the observed thermal radio flux from the nearby cloud, 3(1049) ionizing photons s-1. Commensurately, it produces 107.8 \Lsun in total luminosity, providing the heating source for the nearby molecular cloud, L_cloud 107 \Lsun. These interactions between a cluster of hot stars and a wayward molecular cloud are similar to those seen in the ``Quintuplet/Sickle'' region. The small spread of formation times for the known young clusters in the Galactic Center, and the relative lack of intermediate-age stars ( tau _age=107.0 to 107.3 yrs), suggest that the Galactic Center has recently been host to a burst of star formation. Finally, we have made new identifications of near-infrared sources that are counterparts to recently identified x-ray and radio sources.