Online reputation management is the practice of monitoring the online reputation of an entity, be it a person, a company, a government or something else and putting actions in place if or when something negative about this entity surfaces.
Let’s say Acme Corporation has a product called Foobarbaz and reports surface online that this product just plain sucks. Of course Acme Corporation is afraid that if their sales will suffer so they go to an online reputation management company (often a SEO company specializing in online reputation management) and they will try to deal with it. They may try to manipulate the SERPS so that bad reviews of that product are not visible when you search for that product or discredit the user in question so that other people who read the review will not believe him/her.