The increasing demand for sustainable and efficient energy storage materials has led to significant research into utilizing waste biomass for producing activated carbons. This study investigates the impact of the structural properties of activated carbons derived from various lignocellulosic biomasses—barley straw, wheat straw, and wheat bran—on the electrochemical performance of supercapacitors. The Fourier Transform Infrared (FTIR) spectroscopy analysis reveals the presence of key functional groups and their transformations during carbonization and activation processes. The Raman spectra provide detailed insights into the structural features and defects in the carbon materials. The electrochemical tests indicate that the activated carbon’s specific capacitance and energy density are influenced by the biomass source. It is shown that the wheat-bran-based electrodes exhibit the highest performance. This research demonstrates the potential of waste-biomass-derived activated carbons as high-performance materials for energy storage applications, contributing to sustainable and efficient supercapacitor development.