The Foundation Supernova Survey aims to provide a large, high-fidelity, homogeneous, and precisely calibrated low-redshift Type Ia supernova (SN Ia) sample for cosmology. The calibration of the current low-redshift SN sample is the largest component of systematic uncertainties for SN cosmology, and new data are necessary to make progress. We present the motivation, survey design, observation strategy, implementation, and first results for the Foundation Supernova Survey. We are using the Pan-STARRS telescope to obtain photometry for up to 800 SNe Ia at z<~0.1. This strategy has several unique advantages: (1) the Pan-STARRS system is a superbly calibrated telescopic system, (2) Pan-STARRS has observed 3/4 of the sky in grizyP1 making future template observations unnecessary, (3) we have a well-tested data-reduction pipeline, and (4) we have observed ~3000 high-redshift SNe Ia on this system. Here, we present our initial sample of 225 SN Ia grizP1 light curves, of which 180 pass all criteria for inclusion in a cosmological sample. The Foundation Supernova Survey already contains more cosmologically useful SNe Ia than all other published low-redshift SN Ia samples combined. We expect that the systematic uncertainties for the Foundation Supernova Sample will be two to three times smaller than other low-redshift samples. We find that our cosmologically useful sample has an intrinsic scatter of 0.111mag, smaller than other low-redshift samples. We perform detailed simulations showing that simply replacing the current low-redshift SN Ia sample with an equally sized Foundation sample will improve the precision on the dark energy equation-of-state parameter by 35 per cent, and the dark energy figure of merit by 72 per cent.