The hybrid library was a term in common use in UK digital library development. It originated in the UK Electronic Libraries Programme, and, I think, was coined by that programme's director, Chris Rusbridge. It was discussed in different ways. The rationale for the term was to get around either-or discussions, and to focus on the fact that libraries had to manage resources in multiple formats. Here is how I described the hybrid library at the time:
We are only in early stages of such developments, but this variety of resource, and of organizational approach, is characteristic of what is coming to be known as the `hybrid library'. The hybrid library can be understood as an organized attempt to come to terms with the multiple islands that library services are increasingly becoming and to reduce the difference in patterns of access and management between those islands. [The library, the catalogue, the broker: brokering access to information in the hybrid library]Such islands might be characterised by technical, policy, systems, and other differences.
I was never particularly fond of the term, as one would expect any working academic library to be hybrid in this sense. The hybrid library however occupied the space between the 'digital library' and its implied companion, the 'non-digital' library and had its uses. A google search (as of today anyway) shows its close association with eLib, the projects it funded, and discussions it influenced.
In this context, I was interested to see the term emerge again. Endeavor recentlly announced its vision for the Hybrid Library System:
"This vision recognizes that while the management of physical assets within libraries is and will continue to be a critical concern, the rapid growth of digital collections is already transforming how library software providers are approaching the market," said Sara Randall, director of strategic products at Endeavor. "As our customers increasingly ingest and manage more digitally-born materials, Endeavor will complement this with expanded solutions that address this trend." [Endeavor news/events - Corporate News]