Anime is the term used to describe a particular style of animated material, one that originated in Japan and is often defined by a broad set of conventions, cliches, and stylistic choices. Such choices often include exaggerated expressions and facial characteristics (such as big eyes). Manga is the term used to described the printed version of such media. While these definitions can be roughly equated with the American concepts of "cartoons" and "comic books," anime and manga have evolved differently in Japan. They are far more popular with a wider variety of age groups, including adults audiences, and many anime and manga titles deal with intellectually mature themes and concepts (for instance, the dissolution of the family, the trauma of war, or the nature of humanity).
If you would like a more comprehensive definition of anime, you are in luck. Most guides to anime and manga begin with their take on that definition. For a quick definition, check out the Anime News Network's definition of Anime. Otherwise there are a number of guides you might wish to check. Robin Brenner's Understanding Manga and Anime (amazon) is an excellent place to begin as well as Gilles Poitras' work Anime Essentials (amazon). The article Anime, manga, and otaku culture: a quick study guide for the uninitiated by Megan Bauer can also be useful.
Anime and manga come from a different culture, use a different language and rely on a whole host of different cultural norms and cues. While you can certainly collect anime and manga without understanding it, you will be doing your patrons and yourself a disservice. Fortunately there are a number of different sources for narrowing this culture gap.
As said before, Robin Brenner's Understanding Manga and Anime (amazon) and Gilles Poitras' work Anime Essentials (amazon) provide an excellent foundation to begin your study. Anime Essentials is particularly easy to understand though it is written primarily for a fan of anime or manga rather than a library professional. Though yet to be released, The Rough Guide to Anime (amazon) by Simon Richmond looks to be another useful source of basic information.
If you are interested in a further exploration of the culture of anime and manga, try Roland Kelts' Japanamerica (amazon) or Antonia Levi's Samurai from Outer Space (amazon). Both of these titles explain Japanese culture in the context of anime and in the context of American culture. For a more scholarly approach, the annual journal Mechademia (web) offers a academic look at different facets of anime and manga. In addition, Anime from Akira to Howl's Moving Castle, Updated Edition (amazon) by Susan Napier offers a sophisticated examination of many of anime's cultural cues.
Cultural Glossaries
If you are simply looking for some quick references, definitions, or explanations, it is difficult to beat Gilles Poitras' glossaries The Anime Companion (amazon) and The Anime Companion 2 (amazon). They provide extensive and well written explanations for many Japanese terms and cultural oddities. If all you need is quick reference, the Anime News Network's lexicon may have the information you need.
Anime as has existed in America for a long time and in a number of different formats, however, it has seen a tremendous growth in popularity over the last ten years. Along with anime, the popularity of manga has exploded, especially with the young adult audience. Consequently material for this young adult audience is what is primarily published in American markets. The impact it has had on the market is undeniable and there have been several articles in journals such as Publisher's Weekly about the impact of anime and manga.
Understanding Manga and Anime (amazon) by Robin Brenner
Anime Essentials (amazon) by Giles Poitras
Anime, manga, and otaku culture: a quick study guide for the uninitiated by Megan Bauer
The Rough Guide to Anime (amazon) by Simon Richmond
Japanamerica (amazon) by Roland Kelts
Samurai from Outer Space (amazon) by Antonia Levi
Anime from Akira to Howl's Moving Castle, Updated Edition (amazon) by Susan Napier
The Anime Companion (amazon) by Gilles Poitras
The Anime Companion 2 (amazon) by Gilles Poitras
Manga sells anime--and vice versa by Calvin Reid
Manga, anime invade the U.S by Douglas Wolk