In bauxite impurities of ${\mathrm{Fe}}_2{\mathrm{O}}_3,{\mathrm{TiO}}_2$ and ${\mathrm{SiO}}_2$ are present, ${\mathrm{Fe}}_2{\mathrm{O}}_3$ and ${\mathrm{TiO}}_2$ are basic oxides therefore does not reacts with or dissolve in $\mathrm{NaOH}$ whereas ${\mathrm{SiO}}_2$ is acidic oxide it gets dissolve in $\mathrm{NaOH}$, hence leach out

${\mathrm{SiO}}_2+2\mathrm{NaOH}\to {\mathrm{Na}}_2{\mathrm{SiO}}_3\left(\mathrm{aq}.\right)+{\mathrm{H}}_2\mathrm{O}$