Your role as an admiral of a star fleet puts you in a high ranked position among the ruling leaders. Depending on the type of government you will have to get along with you ruling party. The reputation points score how well you are received amongst the government. The score ranges from 0 to 100, with 0 meaning that you will be fired imminently. To gain reputation you have a couple of choices
a higher reputation score will increase the yearly budget you are allotted for fleet and research development.
The political tension score is an indicator of how well 2 nations/races get along. Tension scores range from 0-100 with a score above 80 meaning the nations are at war.