You check references to see what you can find out about a candidate that you are seriously considering. How hard do they work? Are they reliable? Skills, Character, History. What does their overall brand say about them?
If there are problems or red flags you are more likely to pass. If the brand is strong, a positive compelling story, you are more likely to hire.
The story is the same from the other direction. Candidates do research on companies they are considering. They talk to people, search for information, ask around. Your brand matters and if the story is negative,