A dredge-up is any one of several stages in the evolution of some stars. By definition, during a dredge-up, a convection zone extends all the way from the star's surface down to the layers of material that have undergone fusion. Consequently, the fusion products are mixed into the outer layers of the star's atmosphere, where they can be seen in stellar spectra.
The second dredge-up occurs in stars with 4–8 solar masses. When helium fusion comes to an end at the core, convection mixes the products of the CNO cycle. This second dredge-up causes an increase in the surface abundance of 4He and 14N, whereas the amount of 12C and 16O decreases.
The third dredge-up
The third dredge-up occurs after a star enters the asymptotic giant branch, after a flash occurs in a helium-burning shell. The third dredge-up brings helium, carbon, and the s-process products to the surface, increasing the abundance of carbon relative to oxygen; in some larger stars this is the process that turns the star into a carbon star.
The names of the dredge-ups are set by the evolutionary and structural state of the star in which each occurs, not by the sequence in which they occur in any one star. Some lower-mass stars experience the first and third dredge-ups in their evolution without ever having gone through the second.
Lambert, D.L. (1992). "Observational effects of nucleosynthesis in evolved stars". In Edmunds, Mike G.; Terlevich, Roberto J. (eds.). Elements and the Cosmos. University of Cambridge. pp. 92–109. ISBN 0-521-41475-X.