A non-fiduciary relationship arises when a person uses a possession of yours to benefit themselves. For example, if your business partner invests your money into real estate for the sole purpose of earning himself monetary interest on that property, he is performing a non-fiduciary transaction.
A transaction made by a representative of a business arrangement doesn't have to be unethical. In the case of a non-fiduciary relationship, a financial investment could be made by an individual in the relationship on behalf of the group. If that money belongs to the individual making the investment, he is a non-fiduciary contributor to the transaction.
Banks are a prime example of a fiduciary, or sometimes a non-fiduciary, relationship. If a portfolio manager invests your money so they can bump up the price of the stock to benefit their own portfolio, that would be a non-fiduciary action. In a fiduciary relationship, the fund manager would invest your money with your best interest at heart. Fiduciary relationships usually includes a good-faith agreement between the parties.
Fiduciary came from the Latin word for trust. The fiduciary generally has more knowledge or expertise and often includes a business adviser, attorney, guardian, estate administrator, banker, stockbroker or real estate agent.