While RFC 793 only describes the raw mechanism without even mentioning the term "half closed", RFC 1122 elaborates on that matter in section 4.2.2.13. You may wonder who the hell needs that feature. The designers of TCP also implemented the TCP/IP for the Unix system and, like every Unix user, loved I/O redirection. According to W. Stevens (TCP/IP illustrated, Section 18.5) the desire to I/O-redirect TCP streams was the motivation to introduce the feature. It allows the FIN ack take the role of or be translated as EOF. So it's basically a feature that allows you to casually create impomptu request/response-style interaction on the application layer, where the FIN signals "end of request".