  We study the mean properties of a large representative sample of 217 galaxies
showing CIII] emission at $2<z<4$, selected from a parent sample of $\sim$750
main-sequence star-forming galaxies in the VANDELS survey. These CIII] emitters
have a broad range of UV luminosities, thus allowing a detailed stacking
analysis to characterize their stellar mass, star formation rate (SFR) and
stellar metallicity, as a function of the UV emission line ratios, EWs, and the
carbon-to-oxygen (C/O) abundance ratio. Reliable CIII] detections represent
$\sim$30% of the parent sample. Extreme CIII] emitters
(EW(CIII])$\gtrsim$8\r{A}) are exceedingly rare ($\sim$3%) in VANDELS. The UV
line ratios of the sample suggest no ionization source other than massive
stars. Stacks with larger EW(CIII]) show larger EW(Ly$\alpha$) and lower
metallicity, but not all CIII] emitters are Ly$\alpha$ emitters. The stellar
metallicities of CIII] emitters are not significantly different from that of
the parent sample, increasing from $\sim$10% to $\sim$40% solar for stellar
masses $\log$(M$_{\star}$/M$_{\odot})\sim$9-10.5. The stellar mass-metallicity
relation of the CIII] emitters is consistent with previous works showing strong
evolution from $z=0$ to $z\sim3$. The C/O abundances of the sample range
35%-150% solar, with a noticeable increase with FUV luminosity and a smooth
decrease with the CIII] EW. We discuss the CIII] emitters in the C/O-Fe/H and
the C/O-O/H planes and find they follow stellar and nebular abundance trends
consistent with those of Milky Way halo and thick disc stars and local HII
galaxies, respectively. A qualitative agreement is also found with chemical
evolution models, which suggests that CIII] emitters at $z\sim$3 are
experiencing an active phase of chemical enrichment.
