(Abridged) Palomar Gattini-IR is a new wide-field, near-infrared robotic time domain survey operating at Palomar Observatory. Using a 30 cm telescope mounted with a H2RG detector, Gattini-IR achieves a field of view of 25 sq. deg. with a pixel scale of 8.7 arcsec in J-band. Here, we describe the system design, survey operations, data processing system and on-sky performance of Palomar Gattini-IR. As a part of the nominal survey, Gattini-IR scans $approx 7500$ square degrees of the sky every night to a median 5$sigma$ depth of $15.7$ AB mag outside the Galactic plane. The survey covers $approx 15000$ square degrees of the sky visible from Palomar with a median cadence of 2 days. A real-time data processing system produces stacked science images from dithered raw images taken on sky, together with PSF-fit source catalogs and transient candidates identified from subtractions within a median delay of $approx 4$ hours from the time of observation. The calibrated data products achieve an astrometric accuracy (RMS) of $approx 0.7$ arcsec with respect to Gaia DR2 for sources with S/N $> 10$, and better than $approx 0.35$ arcsec for sources brighter than $approx 12$ Vega mag. The photometric accuracy (RMS) achieved in the PSF-fit source catalogs is better than $approx 3$% for sources brighter than $approx 12$ Vega mag, as calibrated against the 2MASS catalog. With a field of view $approx 40times$ larger than any other existing near infrared imaging instrument, Gattini-IR is probing the reddest and dustiest transients in the local universe such as dust obscured supernovae in nearby galaxies, novae behind large columns of extinction within the galaxy, reddened micro-lensing events in the Galactic plane and variability from cool and dust obscured stars. We present results from transients and variables identified since the start of the commissioning period.