"Conflict of interest" describes a situation where a journalist's professional obligations to present a full and fair picture to readers is in conflict with a personal obligation or interest. For instance: A journalist writing a story about the company where his or her spouse is the CEO. Making the company look bad would presumably be bad for the journalist's marriage (and family income); this isn't to say that the journalist might not write a full and fair story-- only that the situation puts the journalist in a situation where there's pressure to do otherwise.
"Disclosure" is the practice among journalists of disclosing possible conflicts of interest-- first to an editor (if you've got one), who might re-assign the story to someone else, and then (if the journalist stays on the story despite the possible conflict) to readers in the text of the story itself.