1540s, "belief, faith," from Middle French crédit (15c.) "belief, trust," from Italian credito, from Latin creditum "a loan, thing entrusted to another," neuter past participle of credere "to trust, entrust, believe" (see credo).
The commercial sense of "confidence in the ability and intention of a purchaser or borrower to make payment at some future time" was in English by 1570s (creditor is mid-15c.); hence "sum placed at a person's disposal" by a bank, etc., 1660s. From 1580s as "one who or that which brings honor or reputation to." Meaning "honor, acknowledgment of merit," is from c. 1600.
Academic sense of "point awarded for completing a course of study" is by 1904 (short for hour of credit (1892), given for satisfactory completion of one lecture, etc., a week, usually one hour in length). Movie/broadcasting sense "acknowledgement and naming of the individual contributors" (in plural, credits) is by 1914.
Credit rating is from 1958; credit union "cooperative banking society" is 1881, American English.