Footnotes and endnotes are the two most common ways of citing academic text. Some people also refer to endnotes as "backnotes," although it is not a term commonly used. Essentially, endnotes, or backnotes, are a means of identifying the sources of the information you either quote or refer to in your academic papers.
When using end/backnotes, each use of a source, either as a quotation, paraphrase, or other reference, is numbered in consecutive order with an Arabic numeral ( 1, 2, 3, 4, etc) that corresponds to the same Arabic number on a separate Endnotes, or Backnotes, page that will be appended to your essay or other academic paper. In the backnote, following the appropriate and consecutively ordered Arabic number, you will provide standard citation information in whatever academic writing style your instructor prefers, be that MLA, APA, or otherwise.
Standard citation information includes things like author, title of book, title of article, editor of collection, Web site name, date of retrieval from the Internet, date of publication etc. So, backnotes, more commonly called endnotes, provide a consecutively numbered list providing all the information required for identifying and crediting sources and corresponding to identically numbered quotations, paraphrases, etc. drawn from sources used as support or explanation or background etc. in your academic paper.
Your instructor may also require other source identification like Works Cited or Bibliography to accompany the end/backnotes page. In addition, instructors may request that end/backnotes also be annotated, which means that you would comment upon the sources you have used, perhaps stating the strong or weak points or the authors' unique qualifications, etc.
I have not heard of the term "backnotes" before. Is it possible your teacher was talking about footnotes or endnotes?
Footnotes are notes that are at the bottom of the page. You may have seen superscript numbers when reading books before. A superscript number is a small number that is above the text, like how you write the number 2 when squaring something in math. You can use footnotes in your essay to provide more information about the subject (or where to find more information about the subject), to show a quote or viewpoint, or as an alternative to doing your citations in parenthesis.
Endnotes would be located at the end of your essay. They serve the same purpose as footnotes, but you don't have to jump back and forth between reading the essay and reading the footnotes.
Hopefully your teacher was referring to either footnotes or endnotes and this helps! If you provide some more information about your essay topic, you should be able to get some more specific examples :)