This is the final version of the article. It first appeared from EDP Sciences via http://dx.doi.org/10.1051/0004-6361/201628169 ; Aims. We present observations from the Gaia-ESO Survey in the lines of H?, [N II], [S II], and He I of nebular emission in the central part of the Carina Nebula. Methods. We investigate the properties of the two already known kinematic components (approaching and receding), which account for the bulk of emission. Moreover, we investigate the features of the much less known low-intensity high-velocity (absolute RV >50 km/s) gas emission. Results. We show that gas giving rise to H? and He I emission is dynamically well correlated with but not identical to gas seen through forbidden-line emission. Gas temperatures are derived from line-width ratios, and densities from [S II] doublet ratios. The spatial variation of N ionization is also studied, and found to differ between the approaching and receding components. The main result is that the bulk of the emission lines in the central part of Carina arise from several distinct shell-like expanding regions, the most evident found around ? Car, the Trumpler 14 core, and the star WR25. These ?shells? are non-spherical and show distortions probably caused by collisions with other shells or colder, higher-density gas. Some of them are also partially obscured by foreground dust lanes, while very little dust is found in their interior. Preferential directions, parallel to the dark dust lanes, are found in the shell geometries and physical properties, probably related to strong density gradients in the studied region. We also find evidence that the ionizing flux emerging from ? Car and the surrounding Homunculus nebula varies with polar angle. The high-velocity components in the wings of H? are found to arise from expanding dust reflecting the ? Car spectrum. ; We wish to thank an anonymous referee for the helpful suggestions. This research is based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 188.B- 3002. These data products have been processed by the Cambridge Astronomy Survey Unit (CASU) at the Institute of Astronomy, University of Cambridge, and by the FLAMES/UVES reduction team at INAF/Osservatorio Astrofisico di Arcetri. These data have been obtained from the Gaia-ESO Survey Data Archive, prepared and hosted by the Wide Field Astronomy Unit, Institute for Astronomy, University of Edinburgh, which is funded by the UK Science and Technology Facilities Council. This work was partly supported by the European Union FP7 programme through ERC grant number 320360 and by the Leverhulme Trust through grant RPG-2012-541. We acknowledge the support from INAF and Ministero dell?Istruzione, dell?Universit? e della Ricerca (MIUR) in the form of the grant ?Premiale VLT 2012?. The results presented here benefit from discussions held during the Gaia-ESO workshops and conferences supported by the European Science Foundation through the GREAT Research Network Programme. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.