To denigrate is to say bad things — true or false — about a person or thing. Your reputation as a math whiz might be hurt if your jealous classmate manages to denigrate you, even though the accusations are unfounded.
The verb denigrate comes from the Latin word denigrare, which means “to blacken.” To sully or defame someone’s reputation, or to spread negative or hurtful information about a company or a situation, is to denigrate it. Your neighbors may denigrate your proposal for mandatory recycling in an attempt to stop your plan. Denigrate can also mean that you're making something seem less important, like when your brother tries to denigrate your athletic achievements.