The vestigial structures are the remnants of the evolutionary past of the organism which continues to persist in the modern forms however, they are either atrophied, rudimentary or degenerate.
These structures have either lost their functionality in the modern organisms or if they retain any function it is mostly different from the original function and much reduced.
An example of the vestigial structure is plica semilunaris which is a small fold present in the inner corner of the eye and it is a remnant of the nictating membrane in the early organisms.