We present an analysis of a deep (1σ=13 μJy) cosmological 1.2 mm continuum map based on ASPECS, the ALMA Spectroscopic Survey in the Hubble Ultra Deep Field. In the 1 arcmin 2 covered by ASPECS we detect nine sources at s >3.5 significance at 1.2 mm. Our ALMA-selected sample has a median redshift of = z 1.6 0.4, with only one galaxy detected at z>2 within the survey area. This value is significantly lower than that found in millimeter samples selected at a higher flux density cutoff and similar frequencies. Most galaxies have specific star formation rates (SFRs) similar to that of main-sequence galaxies at the same epoch, and we find median values of stellar mass and SFRs of , respectively. Using the dust emission as a tracer for the interstellar medium (ISM) mass, we derive depletion times that are typically longer than 300 Myr, and we find molecular gas fractions ranging from ∼0.1 to 1.0. As noted by previous studies, these values are lower than those using CO-based ISM estimates by a factor of ∼2. The 1 mm number counts (corrected for fidelity and completeness) are in agreement with previous studies that were typically restricted to brighter sources. With our individual detections only, we recover 55%±4% of the extragalactic background light (EBL) at 1.2 mm measured by the Planck satellite, and we recover 80% ±7% of this EBL if we include the bright end of the number counts and additional detections from stacking. The stacked contribution is dominated by galaxies at -z 1 2, with stellar masses of (1-3)×10 10 M . For the first time, we are able to characterize the population of galaxies that dominate the EBL at 1.2 mm.