The following is used from the Purdue OWL website.
A bibliography is a list of sources (books, journals, websites, periodicals, etc.) one has used for researching a topic. Bibliographies are sometimes called "references" or "works cited" depending on the style format you are using. A bibliography usually just includes the bibliographic information (i.e., the author, title, publisher, etc.).
An annotation is a summary and/or evaluation. Therefore, an annotated bibliography includes a summary and/or evaluation of each of the sources. Depending on your project or the assignment, your annotations may do one or more of the following:
Why should I write an annotated bibliography?
The bibliographic information: Generally, though, the bibliographic information of the source (the title, author, publisher, date, etc.) is written in either MLA or APA format.
The annotations: The annotations for each source are written in paragraph form. The lengths of the annotations can vary significantly from a couple of sentences to a couple of pages. The length will depend on the purpose. If you're just writing summaries of your sources, the annotations may not be very long. However, if you are writing an extensive analysis of each source, you'll need more space.
You can focus your annotations for your own needs or for the needs of your instructor. A few sentences of general summary followed by several sentences of how you can fit the work into your larger paper or project can serve you well when you go to draft
Annotated bibliographies for the composition classes show your instructor that you have evaluated the sources that you are thinking of using for an essay that requires primary and/or secondary sources. While the annotated bibliography is an evaluation of sources and their relevance to your actual essay topic, using the information from these sources will look a little differently in the context of the essay with an overall thesis.