We present and discuss the results of the Herschel Gould Belt survey (HGBS) observations in an 11 deg2 area of the Aquila molecular cloud complex at d 260 pc, imaged with the SPIRE and PACS photometric cameras in parallel mode from 70 μm to 500 μm. Using the multi-scale, multi-wavelength source extraction algorithm getsources, we identify a complete sample of starless dense cores and embedded (Class 0-I) protostars in this region, and analyze their global properties and spatial distributions. We find a total of 651 starless cores, 60% ± 10% of which are gravitationally bound prestellar cores, and they will likely form stars inthe future. We also detect 58 protostellar cores. The core mass function (CMF) derived for the large population of prestellar cores is very similar in shape to the stellar initial mass function (IMF), confirming earlier findings on a much stronger statistical basis and supporting the view that there is a close physical link between the stellar IMF and the prestellar CMF. The global shift in mass scale observed between the CMF and the IMF is consistent with a typical star formation efficiency of 40% at the level of an individual core. By comparing the numbers of starless cores in various density bins to the number of young stellar objects (YSOs), we estimate that the lifetime of prestellar cores is 1 Myr, which is typically 4 times longer than the core free-fall time, and that it decreases with average core density. We find a strong correlation between the spatial distribution of prestellar cores and the densest filaments observed in the Aquila complex. About 90% of the Herschel-identified prestellar cores are located above a background column density corresponding to AV 7, and 75% of them lie within filamentary structures with supercritical masses per unit length ≳16 M⊙/pc. These findings support a picture wherein the cores making up the peak of the CMF (and probably responsible for the base of the IMF) result primarily from the gravitational fragmentation of marginally supercritical filaments. Given that filaments appear to dominate the mass budget of dense gas at AV> 7, our findings also suggest that the physics of prestellar core formation within filaments is responsible for a characteristic "efficiency" {SFR/M_dense ˜ 5+2-2 × 10-8 yr-1} for the star formation process in dense gas.Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.Figures 18, 19, and Appendices are available in electronic form at http://www.aanda.orgHerschel column density and temperature maps (FITS format) and full Tables A.1 and A.2 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/584/A91< Réduire