Utilizing the high-resolution, large-scale LAOZI cosmological simulations we investigate the nature of the metal-poor (${rm [Z/H]<-2}$) damped Lyman alpha systems (mpDLA) at $z=3$. The following physical picture of mpDLAs emerges. The majority of mpDLAs inhabit regions $ge 20$~kpc from the host galaxy center on infalling cold gas streams originating from the intergalactic medium, with infall velocity of $sim 100$ km/s and temperature of $sim 10^{4}$ K. For each host galaxy, on average, about $1%$ of the area within a radius $150$~kpc is covered by mpDLAs. The mpDLAs are relatively diffuse ($n_{rm{gas}} sim 10^{-2}$ cm$^{-3}$), Jeans quasi-stable, and have very low star formation rate ($dot{Sigma} le 10^{-4} M_{odot} rm{ yr}^{-1} rm{ kpc}^{-2}$). As mpDLAs migrate inward to the galaxy center, they mix with high metallicity gas and stellar outflows in the process, removing themselves from the metal-poor category and rendering the central ($le 5$ kpc) regions of galaxies devoid of mpDLAs. Thus, the central regions of the host galaxies are populated by mostly metal-rich DLAs instead of mpDLAs. All observables of the simulated mpDLAs are in excellent agreement with observations, except the gas density, which is about a factor of ten lower than the value inferred observationally. However, the observationally inferred value is based on simplified assumptions that are not borne out in the simulations.