Some basis sets are said to be "correlation consistent". What does it mean in practice ?
Wikipedia has an answer here:
Edit: adding introductory text from Wikipedia:
Some of the most widely used basis sets are those developed by Dunning and coworkers, since they are designed to converge systematically to the complete-basis-set (CBS) limit using empirical extrapolation techniques. For first- and second-row atoms, the basis sets are cc-pVNZ where N=D,T,Q,5,6,... (D=double, T=triples, etc.). The 'cc-p', stands for 'correlation-consistent polarized' and the 'V' indicates they are valence-only basis sets. They include successively larger shells of polarization (correlating) functions (d, f, g, etc.). More recently these 'correlation-consistent polarized' basis sets have become widely used and are the current state of the art for correlated or post-Hartree-Fock calculations.
I recommend reading Thom Dunning Jr. “Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen.” J. Chem. Phys. 90, 1007 (1989) by for an answer to this question.
The abstract says the following:
This leads to the concept of correlation consistent basis sets, i.e., sets which include all functions in a given group as well as all functions in any higher groups.
This refers to the telescoping nature of the angular momentum levels used, e.g. 5s4p3d2f1g.