What do you understand by the term variable valency?

Variable Valency: In the case of the atoms of transition elements, ions formed after the loss of valency electrons do not possess a stable core as the configuration of the outermost shell is not ${\mathrm{ns}}^2{\mathrm{np}}^6$ but$\left({\mathrm{ns}}^2{\mathrm{np}}^6{\mathrm{nd}}^{1-10}\right)$. This shell generally loses one or more electrons giving rise to metal ions of higher valencies.

The transition elements show variable valency involving valence electrons and d-electrons of the penultimate energy shell. The common valence of transition metals is either 2 or 3.