In acid solution, the reaction ${{\mathrm{MnO}}_4}^{-}\to {\mathrm{Mn}}^{2+}$ involves

Reduction of Manganese:

• The oxidation state of $\mathrm{Mn}$ in ${\mathrm{MnO}}_4^{-}$ is $+7$
• The oxidation state of $\mathrm{Mn}$ in ${\mathrm{Mn}}^{+2}$ is $+2$.
• The oxidation state is getting reduced which is possible in the case of reduction.
• ${{\mathrm{MnO}}_4}^{-}+5{\mathrm{e}}^{-}\to {\mathrm{Mn}}^{2+}$(In acidic medium)

Hence, $\mathrm{Mn}$ goes from $+7$ oxidation state to $+2$ oxidation state, which shows that it is a reduction process.