I was really only kidding about tickets... thats a separate record all together. Thats the DMV record.
These background checks are really for anyone in close contact with children. I've had to get them done for various reasons and none of them have to do with driving. I've had them done for volunteer work, teaching, working in a daycare setting, and now working with middle schoolers.
I'm glad to hear that the library is being proactive in this case. For example, in our church everyone who is in the childrens ministry has to do a background check. Everyone from the nursery workers changing diapers to the teens, has to get it donw. Its not that they don't trust members of the children's staff, but it is for protection for the parents, church, and others.
Really a background check is nothing to be worried about. Are you getting fingerprinted? I've had two fingerprintings, and also two or three Childlines as well... Childlines are the reporting authority for abusive adults. If you abused a child, it will show up on a Childline.