We analyze the CIII ] - \lambda 1908Å emission properties in a sample of 3899 star-forming galaxies ( SFGs ) at 2 < z < 3.8 drawn from the VIMOS Ultra-Deep Survey ( VUDS ) . We find a median equivalent width EW ( CIII ] ) =2.0 \pm 0.2 to 2.2 \pm 0.2Å for the whole SFG population at 2 < z < 3 and 3 < z < 4 , respectively . About 24 % of SFGs are showing EW ( CIII ] ) > 3Å , including \sim 20 % with modest emission 3 < EW ( CIII ] ) < 10Å and \sim 4 % with strong emission EW ( CIII ] ) > 10Å . A small but significant fraction of 1.2 % of SFGs presents strong CIII ] emission 20 < EW ( CIII ] ) < 40Å , with the four strongest emitters ( EW ( CIII ] ) > 40Å up to \sim 95Å ) being associated with broad-line quasars . While this makes CIII ] the second most-frequent emission line in the UV rest-frame spectra of SFGs after Lyman- \alpha , this line alone can not be considered an efficient substitute to measure a galaxy redshift in the absence of Ly \alpha emission , unless the spectral resolution is R > 3000 to distinguish among different possible doublets . We find a large dispersion in the weak correlation between EW ( CIII ] ) and EW ( Ly \alpha ) , with galaxies showing strong CIII ] and no Ly \alpha , and vice-versa . The spectra of SFGs with 10 < EW ( CIII ] ) < 40Å present strong emission lines including CIV- \lambda 1549 , HeII- \lambda 1640 , OIII- \lambda 1664 , but also weaker emission features of highly ionized elements like SiIV- \lambda 1403 , NIV- \lambda 1485 , NIII- \lambda 1750 , or SiIII- \lambda 1888 , indicating the presence of a hard radiation field . We present a broad range of observational evidence supporting the presence of AGN in the strong CIII ] emitting population . As EW ( CIII ] ) is rising , we identify increasingly powerful outflows with velocities up to \sim 1014 km/s , beyond what stellar winds are commonly producing . The strongest CIII ] emitters are preferentially located below the main sequence of star-forming galaxies , with the median star formation rate being reduced by a factor of two . In addition , we find that the median stellar age of the strongest emitters is \sim 0.8 Gyr , about three times that of galaxies with EW ( CIII ] ) < 10Å . X-ray stacked imaging of the strong CIII ] emitters sample show a marginal 2 \sigma detection consistent with low luminosity AGN log ( L _ { X } ( 2 - 10 keV ) ) \sim 42.9 erg/s . Spectral line analysis and classification presented in a joint paper by Nakajima et al . ( 2017 ) confirms that the strongest emitters require the presence of an AGN . We conclude that these properties are indicative of AGN feedback acting in SFGs at 2 < z < 3.8 , contributing to star-formation quenching . We find that quenching timescales of \sim 0.25 - 0.5 \times 10 ^ { 9 } years , are necessary for such AGN feedback to turn part of the star-forming galaxy population with M _ { star } > 10 ^ { 10 } M _ { \odot } at z \sim 3 into the population of quiescent galaxies observed at redshift z \sim 1 - 2 .