Our studies evidence an anisotropic magnetic order below $T_N = 32$~K. Susceptibility data in small fields of about 1~T reveal an antiferromagnetic (AFM) order for $H perp c$, whereas for $H parallel c$ the data are reminiscent of a field-induced ferromagnetic (FM) structure. At low temperatures and for $H perp c$, the field-dependent magnetization and AC susceptibility data evidence a metamagnetic transition at $H^+ = 5$~T, which is absent for $H parallel c$. We assign this to a transition from a planar cycloidal spin structure at low fields to a planar fan-like arrangement above $H^+$. A fully FM polarized state is obtained above the saturation field of $H_{perp S} = 23.7$~T at 2~K with a magnetization of $M_s = 2.8$~$mu_{rm B}{rm /Cr}$. For $H parallel c$, $M(H)$ monotonously increases and saturates at the same $M_s$ value at $H_{parallel S} = 25.1$~T at 4.2~K. Above $T_N $, the magnetic susceptibility and specific heat indicate signatures of two dimensional (2D) frustration related to the presence of planar ferromagnetic and antiferromagnetic exchange interactions. We found a pronounced nearly isotropic maximum in both properties at about $T^* = 45$~K, which is a clear fingerprint of short-range correlations and emergent spin fluctuations. Calculations based on a planar 2D Heisenberg model support our experimental findings and suggest a predominant FM exchange among nearest and AFM exchange among third-nearest neighbors. Only a minor contribution might be assigned to the antisymmetric Dzyaloshinskii-Moriya interaction possible related to the non-centrosymmetric polar space group $R3m$. Due to these competing interactions, the magnetism in AgCrSe$_{2}$, in contrast to the oxygen based delafossites, can be tuned by relatively small, experimentally accessible, magnetic fields, allowing us to establish the complete anisotropic magnetic $H-T$ phase diagram in detail.
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