Arthur was the husband of Chloe. They owned a bed and breakfast.
Arthur and Chloe died every day; more specifically, every night a version of Arthur was killed by the next version of Arthur. The next version would come to the window and knock, and the current version would go outside to meet his fate. The same thing happened with Chloe and with Henrietta, their hen. Arthur was obsessed with finding the best dying words, and spent each day poring through his books to find a great quote.
When the Sixth Doctor came to the bed and breakfast, he too became involved in the daily deaths. After several days, he finally decided not to go the window when his next self knocked. The cycle of deaths was ended. Arthur and Chloe resumed their normal lives. (PROSE: The Death of Me)