A simple activation method has been used to obtain porous carbon material from walnut shells. The effect of the activation duration at 400 °C in an atmosphere with limited air access on the structural, morphological, and electrochemical properties of the porous carbon material obtained from walnut shells has been studied. Moreover, the structure and morphology of the original and activated carbon samples have been characterized by SAXS, low-temperature adsorption porosimetry, SEM, and Raman spectroscopy. Therefore, the results indicate that increasing the duration of activation at a constant temperature results in a reduction in the thickness values of interplanar spacing (d002) in a range of 0.38–0.36 nm and lateral dimensions of the graphite crystallite from 3.79 to 2.52 nm. It has been demonstrated that thermal activation allows for an approximate doubling of the specific SBET surface area of the original carbon material and contributes to the development of its mesoporous structure, with a relative mesopore content of approximately 75–78% and an average pore diameter of about 5 nm. The fractal dimension of the obtained carbon materials was calculated using the Frenkel–Halsey–Hill method; it shows that its values for thermally activated samples (2.52, 2.69) are significantly higher than for the original sample (2.17). Thus, the porous carbon materials obtained were used to fabricate electrodes for electrochemical capacitors. Electrochemical investigations of these cells in a 6 M KOH aqueous electrolyte were conducted by cyclic voltammetry, galvanostatic charge/discharge, and impedance spectroscopy. Consequently, it was established that the carbon material activated at 400 °C for 2 h exhibits a specific capacity of approximately 110–130 F/g at a discharge current density ranging from 4 to 100 mA/g.