What is the type of library you are trying to open? Do you want to open an Aperture library with Aperture or an iPhoto Library, that you have been using with Aperture?
If it is an iPhoto Library, do as the error message says and open the Library in iPhoto first to upgrade it to version 9.4.2:
- Launch iPhoto with the options-key ⌥ held down and from the open panel select the library, that you want o open.
- After opening and upgrading the library quit iPhoto again and now lauch Aperture again; also with the options-key ⌥ held down to select the library. Can you open it now?
If opening and upgrading the library in iPhoto does not help, you probably need to repair the iPhoto Library package of the Library in question - perhaps the file "dataModel.plist" is damaged. To do this you will need to restore this file inside the Library from your backup - see this post by joeholmes: