Your relations with the other cities, and Hades, are measures of how liked or disliked you are by the general populous of a place.
The main commands to use regarding relations are 'relations', which tells you what your own relations are, 'rwho', which tells you of some people very liked or disliked by your city, and if you are an emperor, 'pardon', 'favour' and 'condemn', which remove dislike, improve relations and worsen relations with a specific person respectively.
Relations can be improved by doing good deeds for a city, such as giving food and money to their poor, and reduced by doing bad deeds against a city, such as killing members of the race who lives there.
Doing negative things against a city can also improve your relations with other cities which dislike that city.
Thul'Mar traditionally dislikes everyone else.