It literally means "to hit or strike." It's the past participle of "to smite." (Well, one of them; the other is "smote.") "To smite" is an archaic word meaning to hit or strike, particularly in battle. You hear it most often in stories, tales, and legends of medieval knights. The dragon was smitten by St. George. Jack London, writing about the freezing cold Arctic, wrote: "The cold of space smote the unprotected tip of the planet, and he, being on that unprotected tip, received the full force of the blow."
It carries an idea of intensity and violence. Europe was smitten by the Black Death. The tree was smitten by the thunderbolt.
So, figuratively, it can mean to "strike" with deep feeling. It is often used to mean "struck" romantically. So can other some expressions that literally mean "hit."
"She seems very smitten by him."
"He was bowled over by her."
"She found him stunning."
"He looked at her and was thunderstruck."
I wouldn't use it to mean "happy" because it conveys the ideas of intensity, surprise, and a feeling so strong and intense that it is difficult to think clearly. It is, figuratively, violent.