The word "source" can be used in many ways. In the broadest sense, the source of something is its origin, where it came from, where you found it.
According to PROFESSIONAL GENEALOGY: A MANUAL FOR RESEARCHERS, WRITERS, EDITORS, LECTURERS, AND LIBRARIANS, Elizabeth Shown Mills, ed., Baltimore, Maryland, 2001, p. 332, "Sources, in the genealogical context, are any means (person, document, book, artifact, or repository) through which we acquire information . . ."
We may have several different things in mind when we speak of the source of information.
The original observer of the fact, discoverer of the scientific discovery, etc.
The original publication in which the information was documented.
The book that first summarized this and other related pieces of information.
The person who first told you about the book.
The on-line web page you found, that had a transcript of the information.
Somebody's gedcom file into which they had typed what they read off the web page.
Many others.
You will hear about "primary" sources and "secondary" sources. They differ only very slightly from what you may hear as "original" and "derivative" sources. A primary source was recorded/ documented/ reported as an eye-witness account. It was recorded about a particular event as soon as possible after the event occurred, by someone who was there and in a position to know what was happening without having to rely on anyone else's testimony. All other sources of information are secondary. The original information may have been passed on by someone who made a copy of it (transcript), included it in a book, wrote a letter about it, stated it as a fact in email, posted it on a genealogy forum, or included it in their gedcom file that they are making available for downloading from the Internet. These are "derivative" works because they are derived ultimately from some primary source. Note that a given document could be a primary source for some of its contents, and a secondary source for other parts.
Primary vs. secondary source information can change with time, also. The memory of the scientist who made a discovery was the original (primary) source, but as time passed, the paper she wrote while the discovery was fresh in her mind became more reliable than what she remembered about it. The paper is the primary source, though not the original source.
The value of secondary source material increases greatly as you find information from multiple, independent sources that is self-consistent and in agreement as to what the facts are. But no matter how much secondary source material you accumulate, it can not add up to better evidence, stronger evidence, than the primary source material from which it was derived. The reasoning is, suppose the person who first transcribed the information out of an old family Bible read something wrong. That's one error. Then suppose the person who typed the transcription into an html document so it could be put on a web page made a typing error. That's two. Then the person who found it on the web and typed it into his family tree file made another typing error. That's three. You import his gedcom file into your family tree. Gee, I wonder what it really said in the family Bible?! Clearly, the more time that has passed and the more hands the information has passed through, the more opportunities for error there have been.
There is one situation where having both the primary and secondary source material is advantageous. The secondary source(s) may discuss the information more than does the primary source. The secondary source may help put the information in perspective, assist in its interpretation, or show how it compares to other information. The bottom line is therefore - all sources are important and all sources should be recorded and cited, not only the primary source!
CITING SOURCES
When you make a statement in your genealogical report or family history, either you are repeating something said by someone else, or you are stating a deduction you made based on information you got somewhere. In short, your genealogy report has become a secondary source to anyone who accepts it, learns from it, or attempts to use it! I am not going to debate ethics or argue for a scientist's values here. I will simply present a claim - that your genealogical statement is close to worthless if you don't give the source(s) of it. You have wasted your time and the reader's. Why? Because either you made your statement up, off the top of your head, or it had sources. If the former, it has no place in a research report. If the latter, you freely chose not to give the source. There are several unpleasant possibilities: Perhaps you don't trust the source yourself. Or maybe you want to keep other people dependent on your opinion since you are preventing them from checking for themselves. Could it be that you are too lazy to keep track of your sources? In either case, there is no reason for anyone to believe what you stated. Having said all that, I will now ease up a little and allow for what is in fact the most likely reason you didn't list your sources - you didn't realize how important it is! I will make another wild speculation here - every person who one day decided to see if they could "trace the family tree a ways" went along for quite awhile not recording sources, because they thought all that mattered were the facts, not where they found them. I will further bet that every one of those people eventually wished they had recorded sources, and tried at least a little to go back and find the missing ones. When you reach this point, do you know what will be the biggest frustration? Realizing that a huge amount of your information came from people who didn't record their sources for it! Argggghhhh!
You will run into people who think the purpose for citing sources is to attempt to "prove" the correctness of your statement, or at least to convince people that it is correct. That is not the purpose for citing sources. The purpose served by providing sources is to let not only others but also yourself go back and confirm that you did not make errors when you copied information from the source. If the statement in question is your personal deduction, everyone has a right to see and check your reasoning. This may be a good time to point out that there are lots of educated guesses in every family tree, every historical report. There is always the need to choose between conflicting claims in different sources, and there is seldom if ever enough information to be certain of the choice. In short, you take your best guess. There is absolutely nothing wrong with that, as long as it is labeled speculation or a guess! You would still list the sources for the conflicting information, and your reason(s) for the particular choice you made. Don't you wish people had done that in the on line family trees you find all over the Internet? Aren't you impressed when you find one who did?
So how should sources be cited? First, there is not now and never will be, the one and only rightest way. Not even in astrophysics journals! There is only one requirement that must be met - the source is cited in such a way that the reader can find it! You will see citations such as "Giddings, p.102." O.K., let's see you find it! We'll wait! Citations like this occur out of a form of intellectual snobbishness, intentional or otherwise. Everyone properly educated in the field should know who Giddings is, right? And which of his 14 books applies to the topic at hand?
If the source is a book, give the title, author or editor, date and place of publication, publisher, volume if part of a set, chapter only if each chapter is written by a different author, and finally the page. If the source is rare, also give the location where you accessed it (e.g. "National Library of Congress, call number EXC34528".) If the source is a person, it is common to use: "Personal communication from June Cleaver, April 27th, 1968." You may want to indicate why one should believe June Cleaver, for example that she is the granddaughter of the person being written about. There may be some reluctance to use a living person as a cited reference. Then you should ask them what their source was, go check it, and cite that. If you haven't checked it, don't claim it was your source! This is of some importance: if you got your information out of a book (for example), and the book lists a source where the author got the information, cite the book, not the author's source! You only cite the source you got the information from.
If the source is something like a gravestone, (for example a gravestone), then there is only one of it in existence. Don't say "The gravestone of Willard Fitzjennings" and wander away. They need to know that this gravestone is in the Sandhills Recreational Cemetery, Brookings Road and Avenue E, Wilberforce County, NC, or they aren't going to be able to go check it. Bottom line: Ask yourself if you could find the reference, given only what you plan to write in the citation. One last request - don't add a lot of words to a citation that are NOT needed to find it! Source citations are one thing, footnotes and side comments another. Within these guidelines then, write them however you please!