Molarity expresses concentration as amount of substance per unit volume — moles per litre — rather than mass per volume. Converting from one to the other requires the compound's molecular weight: molarity equals grams per litre divided by grams per mole.
It matters because mass is not a count. Research peptides span roughly 700 to 5,000 g/mol, so the same mass of a small peptide and a large one are very different numbers of molecules. Two solutions at 1 mg/mL of different compounds are not comparable; two at 1 mM are.
Because peptides are large, solutions in the low mg/mL range land in the low millimolar range, and working dilutions are usually quoted in micromolar. Converting between them requires the compound's molecular weight.