$\mathrm{KOH}$ is alkaline in nature and it abstracts proton from water and attacking species ${\mathrm{OH}}^{-}$ is formed, which works as a nucleophile.

From vicinal dihalide, it will form diols:  

${\mathrm{CH}}_2{\mathrm{ClCH}}_2\mathrm{Cl}\stackrel{\mathrm{KOH}\left(\mathrm{aqueous}\right)}{\to }\underset{\mathrm{Ethane}-1, 2-\mathrm{diol}}{{\mathrm{HOCH}}_2{\mathrm{CH}}_2\mathrm{OH}}$

From gem dihalide, gem diol is formed, which converts into carbonyl compound after dehydration.

${\mathrm{CH}}_3{\mathrm{CHCl}}_2\stackrel{\mathrm{KOH} \left(\mathrm{aqueous}\right)}{\to } \left[\mathrm{gem} \mathrm{diol}\right] \underset{‐{\mathrm{H}}_2\mathrm{O}}{\to }\underset{\mathrm{Ethanal}}{{\mathrm{CH}}_3\mathrm{CHO}}$