This may be self-explanatory, but the importance of libraries to an author is simply beyond calculation. In my opinion, it is essential to give back to them whenever possible.
Last week I gave a series of talks on Writing and Illustrating books in several libraries in Osceola County, Florida. Besides bringing inspiration to the next generation, one huge benefit to this is being able to read my work to a great test audience.
It wasn't until I was in 7th grade that I met a professional children's book author. The downtown library where I grew up (in Warren, Ohio) actually had acclaimed author Cynthia Rylant come as part of a calendar contest, which I happened to win, and the brief experience made a major impact on my life.