Something peculiar is notably unusual. If your friend starts saying strange things you don't understand, ask her why she's suddenly become peculiar.
Peculiar comes from the Latin peculiaris, meaning one's own, or personal. In English, it originally meant belonging to one person, private, like your fondness for your peculiar hairbrush. It also had the meaning of something unlike others, special, or remarkable. Eventually we mostly stopped using it for belongings, instead using peculiar to mean unusual or odd.