All these 3 libraries allow to manipulate history object. OK, backbone does a lot of more but let consider only it history part.
What is a difference between these 3 implementation?
History.js is more of a polyfil for browsers that do not natively support HTML5 pushState and for ironing out the differences between different browser implementations of pushState.
Davis.js is a routing layer, primarily on top of pushState (although this can be switched out easily to hash routing). It gives you a simple api to define and respond to routes within your application.
Backbone's router is similar to Davis, however it tries to automatically fall back to hash based routing when pushState is not available.
As the author of Davis I'm slightly biased but I think the Davis api is slightly nicer and more powerful than backbones. I also think that trying to gracefully handle falling back to hash based routing when pushState is not available is not worth the effort and complexity that it can introduce.