godan verb (-su), transitive verb
wear stylishly; dress well
Implies skillfully coordinating clothes to look fashionable, not just putting them on.
彼女はいつもシンプルな服を着こなしている。
She always wears simple clothes stylishly.
スーツを着こなすのは難しい。
It's difficult to wear a suit well.
着る simply means 'to wear' or 'to put on' upper-body garments, while 着こなす adds the nuance of wearing something with style and skill.
Compound of 着 (ki, 'wear') + こなす (konasu, 'handle skillfully'). The exact historical derivation is uncertain, but the combination naturally yields the meaning 'to wear skillfully/stylishly'.