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Palomar Gattini-IR is a new wide-field, near-infrared (NIR) 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 (FOV) of 25 sq. deg. with a pixel scale of 8.″7 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 ≈7500 square degrees of the sky every night to a median 5σ depth of 15.7 AB mag outside the Galactic plane. The survey covers ≈15,000 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 point-spread function (PSF)-fit source catalogs and transient candidates identified from subtractions within a median delay of ≈4 hr from the time of observation. The calibrated data products achieve an astrometric accuracy (rms) of ≈0.″7 with respect to Gaia DR2 for sources with signal-to-noise ratio > 10, and better than ≈0.″35 for sources brighter than ≈12 Vega mag. The photometric accuracy (rms) achieved in the PSF-fit source catalogs is better than ≈3% for sources brighter than ≈12 Vega mag and fainter than the saturation magnitude of ≈8.5 Vega mag, as calibrated against the Two Micron All Sky Survey catalog. The detection efficiency of transient candidates injected into the images is better than 90% for sources brighter than the 5σ limiting magnitude. The photometric recovery precision of injected sources is 3% for sources brighter than 13 mag, and the astrometric recovery rms is ≈0.″9. Reference images generated by stacking several field visits achieve depths of ≳16.5 AB mag over 60% of the sky, while it is limited by confusion in the Galactic plane. With a FOV ≈40× larger than any other existing NIR 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 microlensing 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. [ABSTRACT FROM AUTHOR]