Some journals require you to state the conflicts of interests (if any). According to the Wikipedia definition,

A conflict of interest (COI) is a situation in which a person or organization is involved in multiple interests, financial interest, or otherwise, one of which could possibly corrupt the motivation of the individual or organization.

What exactly is a conflict of interest in the context of journals? How does it affect the publication process? All papers I've read so far has the declaration "The authors declare they have no conflict of interests" in that section. Could anyone give some sample published papers which has a notable conflict of interest in it?