We present optical light curves, redshifts, and classifications for 365 spectroscopically confirmed Type Ia supernovae (SNe Ia) discovered by the Pan-STARRS1 (PS1) Medium Deep Survey. We detail improvements to the PS1 SN photometry, astrometry, and calibration that reduce the systematic uncertainties in the PS1 SN Ia distances. We combine the subset of 279 PS1 SNe Ia (0.03 < z < 0.68) with useful distance estimates of SNe Ia from the Sloan Digital Sky Survey (SDSS), SNLS, and various low-z and Hubble Space Telescope samples to form the largest combined sample of SNe Ia, consisting of a total of 1048 SNe Ia in the range of 0.01 < z < 2.3, which we call the Pantheon Sample. When combining Planck 2015 cosmic microwave background (CMB) measurements with the Pantheon SN sample, we find Wm = 0.307 ± 0.012 and w = -1.026 ± 0.041 for the wCDM model. When the SN and CMB constraints are combined with constraints from BAO and local H0 measurements, the analysis yields the most precise measurement of dark energy to date: w0 = -1.007 ± 0.089 and wa = -0.222 ± 0.407 for the w0waCDM model. Tension with a cosmological constant previously seen in an analysis of PS1 and low-z SNe has diminished after an increase of 2× in the statistics of the PS1 sample, improved calibration and photometry, and stricter light-curve quality cuts. We find that the systematic uncertainties in our measurements of dark energy are almost as large as the statistical uncertainties, primarily due to limitations of modeling the low-redshift sample. This must be addressed for future progress in using SNe Ia to measure dark energy.