Methyl orange is weak organic base. It is used in the titration of strong acid vs weak base.
$\underset{\underset{\left(\mathrm{Y}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{w}\right)}{\mathrm{U}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d }\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}}}{\mathrm{M}\mathrm{e}\mathrm{O}\mathrm{H}}\rightleftharpoons \mathrm{M}{\mathrm{e}}^{+}+\underset{\underset{\left(\mathrm{R}\mathrm{e}\mathrm{d}\right)}{\mathrm{I}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d }\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}}}{\mathrm{O}{\mathrm{H}}^{-}}$
In basic medium, equilibrium lies in backward direction so it shows yellow colour.
In acidic medium, equilibrium shifts in forward direction so colour changes from yellow to red.