I'm reading about this grammar in my book but I don't get it. According to the book it means - そうだ and - らしい. Here is an example:
UPDATE: Full Sentence:
従来、病院といえば白い壁が基調の空間であった。 しかし、白くて冷たい壁を見ていると 人はゆううつな感じになり、不安を覚えるという。 この環境では、患者は快復への意志を高めることはできない。
It says that it is used at the end of a written sentence.
という just means what it always means. と is the quoting particle and いう means "to say". In your example sentence, maybe "It is said that..." would be a fitting translation, i.e.
従来、病院といえば白い壁が基調の空間であった。
Up to now, a hospital was thought of a space with white walls.しかし、白くて冷たい壁を見ていると人はゆううつな感じになり、不安を覚えるという。
But by looking at a white, cold wall, it is said that people start getting depressed and feeling uneasy.この環境では、患者は快復への意志を高めることはできない。
In this environment the patient can't increase his desire for recovery.
"It is said that" is quite close to the nuance of らしい or そうだ, like your textbook points out.
