"Ibid." is an abbreviation of the Latin "ibidem", meaning "in the same place". Because it's an abbreviation, it should always have a '.' on the end, and it may be that the title of this node should have one, too. But will anybody look for it there? I doubt it.
Anyhow, everybody says it's an adverb; you should think of it as "sameplacefully", I suppose.
We use "Ibid." in bibliographies and footnotes, to indicate that the last source we cited is being cited once again. So, on some dark and stormy night, you might cite "Journey to the End of the Night" Is a Load of Old Shite by Susie Bright; in that case, you'd give the title and author, the year of publication, and the name and city1 of the publisher. If the next citation is the same page of the same work, you just say "Ibid." This is cool because the reader doesn't have to compare two long strings to see if it's the same page. This can also be annoying, if the footnotes are on the page bottoms where they belong (endnotes are an abomination) and the last citation was many pages ago; then the reader has to dig back to find out what's going on. I don't know if there's a canonical rule about that, but I'd advise using "Ibid." only if the previous citation to which it refers is right there, in view.
This is not a synonym for the admirable op cit; op cit is when you're referring to the same work, but a different page.
1 I love those: "Bloo Blah Blurkson and Sons,
New York,
London,
Phnom Penh,
Schenectady,
Niscayuna,
Damascus, and
Jonestown." Pure poetry.