They are fictional surveys created by Calvin to show his approval rating for his father, acting out an electoral campaign manager's role towards his candidate. One instance excepted, the polls were invariably very negative, representing Calvin's discontentment (the positive poll was an attempt to call for an "extra push" from Calvin's father).
Calvin used the polls to try and improve his life at home; he anticipated that his father, aiming to re-mediate his low popularity, would give him whatever he wanted (including driving lessons, a shorter school week, later bedtimes, and more allowance) to regain the "public"'s admiration. Calvin often referred to multiple, fictional respondents in the polls, such as "a vast majority of household six-year olds" as opposed to just Hobbes and him.
Calvin's father, naturally, saw right through Calvin's scheme and sarcastically refused every proposition. The polls usually reflected Calvin's father's likeability more than approval for his actual government, although occasionally his indecisiveness and unpopular policies were studied as well.
In The Calvin and Hobbes Tenth Anniversary Book, Bill Watterson explained that the polls Calvin creates are a reflection of how government seems more and more poll-driven to him. In turn, the levelheadedness of Calvin's father may reflect Bill Watterson's own attitude.