Someone who's blowsy is disheveled and frumpy. Your blowsy Aunt Jan might have long, messy hair and wear slightly shabby clothes.
Traditionally, the adjective blowsy has been used mainly to describe dowdy older women, although it sometimes implies a perceivable sexuality as well. You can also describe lush, overblown flowers that are a bit past their peak bloom as blowsy: "I prefer daisies, but my mom is partial to big, blowsy roses." The word dates from the 17th century and comes from a now-obsolete term for "a beggar's female companion," blowze.