In the VisIt source code, `database' refers to code which reads data from a particular file format and converts it into VisIt's internal representation. Currently this internal representation is VTK datasets.
Each database gets its own subdirectory under databases/ in the source tree. Databases are implemented in C++ and compiled to libraries. They are dynamically loaded at application startup; in particular this allows users to have local database implementations which override the globally installed versions.
Here is a Short list of file formats VisIt supports.
Here is a Detailed list of file formats VisIt supports.