Similarly [the] visitor has also shown responsibility to remain within [the] limits of the society he is moving [in], so that he cannot cause any hurt or harm to local culture.

within 是介词，意思是"在...之内"，表示在某个范围或界限内部。 limits 是名词 limit 的复数形式，limit 指"界限、限制"，在这里指社会规范或文化接受的边界。 within the limits 这个短语表示"在界限范围内"，即遵守社会规范、不越界的行为。