The quasi-two-dimensional antiferromagnet Ni2P2S6 belongs to the family of magnetic van der Waals compounds that provides a rich material base for the realization of fundamental models of quantum magnetism in low dimensions. Here, we report high-frequency/high-magnetic field electron spin resonance measurements on single crystals of Ni2P2S6. The results enable one to reliably determine the positive, "easy"-plane type of the single ion anisotropy of the Ni2+ ions with the upper limit of its magnitude 0.7meV. The resonance response reveals strongly anisotropic spin fluctuations setting in shortly above the Néel temperature TN=158K and extending in the antiferromagnetically ordered state down to low temperatures. There, a low-energy magnon excitation gapped from the ground state by only ∼1meV was found. This magnon mode may explain unusual low temperature relaxation processes observed in the latest nuclear magnetic resonance experiments and together with the estimate of the single ion anisotropy they should enable setting up a realistic spin model for an accurate description of magnetic properties of Ni2P2S6.