I'm not sure where to look for the precise definition of "fiduciary".
https://en.wikipedia.org/wiki/Fiduciary fiduciary: A fiduciary is a person who holds a legal or ethical relationship of trust with one or more other parties (person or group of persons).
http://dictionary.law.com/Default.aspx?selected=744 fiduciary: 1) n. from the Latin fiducia, meaning "trust," a person (or a business like a bank or stock brokerage) who has the power and obligation to act for another (often called the beneficiary) under circumstances which require total trust, good faith and honesty. 2) adj. defining a situation or relationship in which a person is acting as a fiduciary for another.
http://dictionary.law.com/Default.aspx?selected=745 fiduciary relationship: n. where one person places complete confidence in another in regard to a particular transaction or one's general affairs or business.
http://dictionary.law.com/Default.aspx?selected=599 duty of care: n. a requirement that a person act toward others and the public with the watchfulness, attention, caution and prudence that a reasonable person in the circumstances would use.
So the business judgment rule isn't where any normal person would want to start on this topic, but I think it's wikipedia article probably is the best in terms of defining a few things and then linking you to more resources.
EDIT: after reading the conservapedia entry on Wesley I found this comment a lot funnier. Unfortunately I couldn't be Mouch, it was said of him that "What I like most about you, Mouch, is that you do not talk too much" and I don't think anyone has ever accused me of that. (: