Methyl orange is weak organic base. It is used in the titration of weak base vs strong acid.

$\underset{\underset{\left(\text{Yellow}\right)}{\text{Unionized form }}}{\mathrm{M}\mathrm{e}\mathrm{O}\mathrm{H}}\rightleftharpoons \mathrm{M}{\mathrm{e}}^{+}+\underset{\underset{\left(\text{Red}\right)}{\text{Ionized form}}}{\mathrm{O}{\mathrm{H}}^{-}}$

In basic medium, equilibrium lies in backward direction and therefore it shows yellow colour.

In acidic medium, equilibrium shifts in forward direction and therefore, colour changes from yellow to red.