Context. Starbursts are one of the main contributors to the chemical enrichment of the interstellar medium. However, mechanisms governing the interaction between the recent star formation and the surrounding gas are not fully understood. Because of their a priori simplicity, the subgroup of H II galaxies constitute an ideal sample to study these mechanisms. Aims: A detailed 2D study of the central region of NGC 5253 has been performed to characterize the stellar and ionized gas structure as well as the extinction distribution, physical properties and kinematics of the ionized gas in the central ~210 pc × 130 pc. Methods: We utilized optical integral field spectroscopy (IFS) data obtained with FLAMES. Results: A detailed extinction map for the ionized gas in NGC 5253 shows that the largest extinction is associated with the prominent Giant H II region. There is an offset of ~0.5 arcsec between the peak of the optical continuum and the extinction peak in agreement with findings in the infrared. We found that stars suffer less extinction than gas by a factor of ~0.33. The [S ii]λ6717/[S ii]λ6731 map shows an electron density (Ne) gradient declining from the peak of emission in Hα (790 cm-3) outwards, while the argon line ratio traces areas with Ne ~ 4200-6200 cm-3. The area polluted with extra nitrogen, as deduced from the excess [N ii]λ6584/Hα, extends up to distances of 3.3 farcsec (~60 pc) from the maximum pollution, which is offset by ~1.5 arcsec from the peak of continuum emission. Wolf-Rayet features are distributed in an irregular pattern over a larger area (~100 pc × 100 pc) and associated with young stellar clusters. We measured He+ abundances over most of the field of view and values of He++/H+ ⪉ 0.0005 in localized areas which do not coincide, in general, with the areas presenting W-R emission or extra nitrogen. The line profiles are complex. Up to three emission components were needed to reproduce them. One of them, associated with the giant H II region, presents supersonic widths and [N ii]λ6584 and [S ii]λλ6717,6731 emission lines shifted up to 40 km s-1 with respect to Hα. Similarly, one of the narrow components presents offsets in the [N ii]λ6584 line of ⪉20 km s-1. This is the first time that maps with such velocity offsets for a starburst galaxy have been presented. The observables in the giant H II region fit with a scenario where the two super stellar clusters (SSCs) produce an outflow that encounters the previously quiescent gas. The south-west part of the FLAMES IFU field is consistent with a more evolved stage where the star clusters have already cleared out their local environment. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile (ESO Programme 078.B-0043).