Wurtzite ferroelectrics possess transformative potential for next-generation microelectronics. A comprehensive understanding of their ferroelectric properties and domain energetics is crucial for tailoring their ferroelectric characteristics and exploiting their functional properties in practical devices. Despite burgeoning interest, the exact configurations, and electronic structures of domain walls in wurtzite ferroelectrics remain elusive. In this work, we elucidate the atomic configurations and electronic properties of electric-field-induced domain walls in ferroelectric ScGaN. By combining transmission electron microscopy and theoretical calculations, a novel charged domain wall with a buckled two-dimensional hexagonal phase is revealed. Density functional theory calculations confirm that such domain wall structures further give rise to unprecedented mid-gap states within the forbidden band. Quantitative analysis unveils a universal charge-compensation mechanism stabilizing antipolar domain walls in ferroelectric materials, wherein the polarization discontinuity at the 180º domain wall is compensated by the unbonded valence electrons. Furthermore, the reconfigurable conductivity of these domain walls is experimentally demonstrated, showcasing their potential for ultra-scaled device applications. Our findings represent a pivotal advancement in understanding the structural and electronic properties of wurtzite ferroelectric domain walls and lay the groundwork for fundamental physics studies and device applications.