The unidentified very-high-energy (VHE; E > 0.1 TeV) gamma -ray source, HESS J1826-130, was discovered with the High Energy Stereoscopic System (HESS) in the Galactic plane. The analysis of 215 h of HESS data has revealed a steady gamma -ray flux from HESS J1826-130, which appears extended with a half-width of 0.21 degrees +/- 0.02 (stat)degrees stat degrees +/- 0.05 (sys)degrees sys degrees . The source spectrum is best fit with either a power-law function with a spectral index Gamma = 1.78 +/- 0.10(stat) +/- 0.20(sys) and an exponential cut-off at 15.2 (+5.5)(-3.2) -3.2+5.5 TeV, or a broken power-law with Gamma (1) = 1.96 +/- 0.06(stat) +/- 0.20(sys), Gamma (2) = 3.59 +/- 0.69(stat) +/- 0.20(sys) for energies below and above E-br = 11.2 +/- 2.7 TeV, respectively. The VHE flux from HESS J1826-130 is contaminated by the extended emission of the bright, nearby pulsar wind nebula, HESS J1825-137, particularly at the low end of the energy spectrum. Leptonic scenarios for the origin of HESS J1826-130 VHE emission related to PSR J1826-1256 are confronted by our spectral and morphological analysis. In a hadronic framework, taking into account the properties of dense gas regions surrounding HESS J1826-130, the source spectrum would imply an astrophysical object capable of accelerating the parent particle population up to greater than or similar to 200 TeV. Our results are also discussed in a multiwavelength context, accounting for both the presence of nearby supernova remnants, molecular clouds, and counterparts detected in radio, X-rays, and TeV energies.