As a financial term, used in such terms as credit card, it refers to the granting of a loan and the creation of debt. Any movement of financial capital is normally quite dependent on credit, which in turn is dependent on the reputation or creditworthiness of the entity which takes responsiblity for the funds. See also credit repair.
A similar usage is in commercial trade, where credit is used to refer to the approval for delayed payments for goods purchased.
In non-fiction writing
In non-fiction writing, especially academic works, it is generally considered important to give credit to sources of information and ideas. Failure to do so often gives rise to charges of plagiarism, and "piracy" of intellectual rights such as the right to receive a royalty for having written. In this sense the financial and individual meanings are linked.
Academic papers generally contain a lengthy section of footnotes or citation. Such detailed crediting of sources provides readers with an opportunity to discover more about the cited material. It also provides a check against misquotation, as it's easy for an attributed quote to be checked when the reference is available. All of this is thought to improve integrity of the instructional capital conveyed, which may be quite fragile, and easy to misinterpret or to misapply.
In creative arts
In the creative arts, credits are an acknowledgement of those that participated in the production. They are often shown at the end of movies and on CD jackets.