Publication information is a catch-all section for "Other Information" that you need to show exactly which version of your source you are getting your information from. For example, if you read one printing of a book and your professor owns a different one, the page numbers might not match up. That could be pretty awkward if your professor looked for one of your quotes and didn't find it! Showing which version helps explain differences in phrases, page numbers, and so on.
For books, you need to know the place of publication, the publisher, and the year the book was published. Look on the inside title page for most of the information (the publisher and city are usually at the bottom). Sometimes the back of the inside title page has the year as part of the copyright statement. If multiple years are listed, you use the most recent. If multiple cities of publication are listed, you usually want the closest one.
See the example box below for a sample of an inside title page.
For articles, the important thing is to write down the information on exactly which magazine, journal, or newspaper your article was in. Write down the date, volume number, issue number, and pages that your article was published on.
Publication information for book chapters is the same as for the whole book: city of publication, publishing company, and year.
Just like everything else, web pages make it complicated to cite the publication information. If there's an issuing group (even if they're also the authoring group) that's a good thing to write down. It's good to record the URL (web address) and the site name that the page was on (which you should already have for the Title). Last, make sure you find the date it was last updated (or write down n.d. for "no date") and the date that you looked at the site. Any additional information that looks like you might need it to find the webpage again is probably helpful.
(Image from the Documenting the American South collection at http://docsouth.unc.edu/)