What is the purpose of melting point in organic chemistry?
It is an important piece of characterizing data.....And thus it aids the identification of unknown organic compounds.
As you will find in organic chemistry laboratories, the quickest way to identify an organic unknown, is to take its melting point (or boiling point), get an idea of the elements it contains, get an idea of what sort of compound it is, acid, amine, amide etc., and then make a few (crystalline) derivatives by standard means.
The melting points of these derivatives are extensively tabulated, and these are available in organic laboratories. It is far quicker than using spectroscopy, which generally will not be definitive anyway, and it will certainly be far cheaper.
Make 2-3 derivatives of an organic unknown, and your melting point data definitively identifies it. It also helps your technique in recrystallization and product purification - something which you have to develop by practice.