Your reputation is your relationship to an entire group of people, such as a town, an organization, or another adventuring party. As you gain the favor or more members of a group, your reputation within that group will increase. When you meet a member of a group for the first time, they may start with a positive relationship to you if you already have a high reputation with a group they are a part of.
Mathematically, your reputation with a group is the sum of all known relationships you have to its members, divided by the number of members, and rounded to the nearest whole number. However, most GMs will not track reputation in this much detail, especially for large groups.
Instead, the GM will often compare the relationships you have to members of a group and make a rough estimate of your reputation when it is needed. If you have a very positive or negative relationship with group members, it's likely that those people have spread the word about you to other people in the group.
The GM should never show numerical reputation values to the players, as this calculation is largely left to the GM's judgment.
Remember that relationships can never govern the actions of player characters, as the player ultimately has the final say in what their character does or says.