Hearsay

Hearsay is, at the most general level, secondhand knowledge, or, any statement made under circumstances that make it impossible to verify, offered at a future point to prove the truth of what was said. The theory behind hearsay is that when someone offers a statement he has heard earlier to prove a fact in contest now, the statement is too removed from reality to be verified by anyone, and thus should be seen as lacking probative value. Hearsay amounts to a principle against gossip: the fact that someone, earlier, heard someone else say something, is inherently unreliable, as subject to invention and the vagaries of memory.

Argumentative Hearsay
Important in court, for sure, hearsay also has some real-life relevance; the hearsay principle mandates that to prove a point currently in controversy, the parties to the dispute should present only facts or statements that can be verified independently, without reference to an earlier situation not observable by all parties to the dispute. The following are examples of hearsay in daily life:
 * Declarant, trying to prove he has the support of more than just himself: "The lurkers agree with me in e-mail." Really?  I can't verify or refute that.  This is hearsay because, first, if the statement has any meaning that the Declarant wants it to have, the underlying facts must be true.  If the lurkers do not actually agree, we shouldn't care.  Thus, the Declarant is offering (1) something that he alone has experienced, (2) to prove that experience, (3) to someone who has not experienced the same facts.  The Declarant's statement depends on its relevance upon a predicate belief that he is telling the truth and remembering the situation correctly.  The Declarant's opponent should not be forced to assume that much.
 * Declarant, trying to prove that he has the Chief Justice's support: "Chief Justice Warren Burger told me, thirty years ago, that what he meant to write in his opinion was that..." The same reasoning.  Unless the Chief Justice actually did agree with the Declarant, the statement is incapable of proving what the Declarant wants it to prove.  However, no-one but Declarant was there to observe the Chief Justice's words; it's unreliable, and we shouldn't be forced to assume the Declarant's truthfulness.

Legally...
Hearsay is an out-of-court statement offered to prove the matter asserted within. To understand hearsay, it is essential to understand why the underlying concept exists: evidence law is predicated on the assumption that statements made outside of the witness stand, unless otherwise proved reliable, are lacking the critical components required to ensure validity (cross-examination, observation of declarant demeanor, and the oath). Therefore, the fact that a statement is made out of court is a proxy for its unreliability as substantive evidence ("substantive" means, "to prove what it says").

Nonhearsay Usage
Although hearsay is presumed inadmissible in court, it is only so presumed insofar as it is offered to prove what it says. However, statements are often offered not to prove what they say, but to prove something else. For example, a nonhearsay usage of an out-of-court statement would be, "the defendant told me he's working with the power company." The statement would not be admissible to prove that the defendant worked for the power company; however, it would be admissible to prove that you thought that he worked for the power company. Other examples exist: when offered to prove a circumstantial state of mind (like the above example), a performative act, or a verbal object, inter alia, a statement is thought to not carry the dangers of hearsay, since its relevance does not depend upon the truth of the matter asserted. Hearsay can also be subject to other bases for challenges that apply to evidence in general, such as being overly prejudicial or obtained illegally.

Admissible Non-Hearsay
Even when a statement is hearsay, it may be admitted in court, provided that external indicia of reliability exist. For example, a person's last words before dying are considered non-hearsay (the dash is important) since a person generally does not lie as their last living act. We think. Generally. A declaration against interest is also thought to be non-hearsay because it is thought that a person does not lie when the lie hurts them.