In order to support new features and enhance security, the database format which is used to store entries and preferences has been changed between major versions. However, much effort has been put into ensuring automatic and transparent upgrading:
In all cases, to read a database generated by a previous version of Password Safe, just open it as you would any database. The entries will be displayed normally, with possible "unknown" values in fields that were unsupported in previous versions (e.g., the creation date of an entry).
When you save such a database, you will be alerted to the fact that the new database will be unreadable by previous version of Password Safe.
You can create versions of the database that are readable by older versions of Password Safe by explicitly exporting to the desired format (File → Export To and select V1 format... or V2 format...). Note that the exported databases will not contain information that was added in newer versions. For example, a version 2 database will not have information regarding the modification times of entries.