The unsteady hydrodynamics of two pitching foils arranged in a side-by-side (parallel) configuration is examined for a range of Strouhal numbers, phase differences, oscillation amplitudes and separation distances. Three distinct vortex patterns are identified in the wake maps, which include separated wake, merged wake and transitional-merged wake. Furthermore, a novel model is introduced based on fundamental flow variables including velocity, location and circulation of dipole structures to quantitatively distinguish vortex patterns in the wake. The physical mechanism of the wake merging process is also elucidated. When an oscillating foil experiences the jet deflection phenomenon, secondary structures separated from the primary street traverse in the other direction by making an angle with its parent vortex street. For in-phase pitching parallel foils, secondary structures from the vortex street of the lower foil interact with the primary vortex street of the upper foil under certain kinematic conditions. This interaction triggers the wake merging process by influencing circulation of coherent structures in the upper part of the wake. It is unveiled that merging of the wakes leads to enhancements in propulsive efficiency by increasing thrust generation without a significant alteration in power requirements. These are attributed to the formation of a high-momentum jet by the merged vortex street, which possesses significantly larger circulation due to the amalgamation of the vortices, and major alterations in the evolution of leading edge vortices. Thus, flow physics, which is thoroughly explored here, is crucial in providing novel insights for the future development of flow control techniques for efficient designs of bio-inspired underwater propulsors.