We present the analysis of new near-infrared, intermediate-resolution spectra of the gravitationally lensed galaxy "the 8 o'clock arc" at zsys = 2.7350 obtained with the X-shooter spectrograph on the Very Large Telescope. These rest-frame optical data, combined with Hubble and Spitzer Space Telescopes images, provide very valuable information, which nicely complement our previous detailed rest-frame UV spectral analysis, and make the 8 o'clock arc one of the better understood "normal" star-forming galaxies at this early epoch of the history of the Universe. From high-resolution HST images, we reconstruct the morphology of the arc in the source plane, and identify that the source is formed of two majors parts, the main galaxy component and a smaller blob separated by 1.2 kpc in projected distance. The blob, with a twice larger magnification factor, is resolved in the X-shooter spectra. The multi-Gaussian fitting of detected nebular emission lines and the spectral energy distribution modeling of the available multi-wavelength photometry provide the census of gaseous and stellar dust extinctions, gas-phase metallicities, star-formation rates (SFRs), and stellar, gas, and dynamical masses for both the main galaxy and the blob. As a result, the 8 o'clock arc shows a marginal trend for a more attenuated ionized gas than stars, and supports a dependence of the dust properties on the SFR. With a high specific star-formation rate, SSFR = 33 ± 19 Gyr-1, this lensed Lyman-break galaxy deviates from the mass-SFR relation, and is characterized by a young age of 40+25-20 Myr and a high gas fraction of about 72%. The 8 o'clock arc satisfies the fundamental mass, SFR, and metallicity relation, and favors that it holds up beyond z ≃ 2.5. We believe that the blob, with a gas mass Mgas = (2.2 ± 0.9) × 109 M&sun; (one order of magnitude lower than the mass of the galaxy), a half-light radius r1/2 = 0.53 ± 0.05 kpc, a star-formation rate SFRHα = 33 ± 19 M&sun; yr-1, and in rotation around the main core of the galaxy, is one of these star-forming clumps commonly observed in z > 1 star-forming galaxies, because it is characterized by very similar physical properties. The knowledge of detailed physical properties of these clumps is a very useful input to models that aim to predict the formation and evolution of these clumps within high-redshift objects. Based on X-shooter observations made with the European Southern Observatory VLT/Kueyen telescope, Paranal, Chile, collected under the programme ID No. 284.A-5006(A).Based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute.