This means you can enable your users to use the same password they are using to logon to your on-premises Active Directory to logon to Windows Azure Active Directory (WAAD).
Password synchronization should not be seen as a replacement for ADFS based federation between your on-premises Active directory and WAAD, but as an alternative for those organization that find it sufficient users have the same password in Office 365 and the on-premises Active Directory. Bear in mind, that password synchronization doen’t support SSO like in transparent SSO (where you authenticate once), but instead will prompt for credentials when the user for instance accesses his mailbox in Exchange Online even though she is logged on to a domain-joined client machine.
For more information about how you enable password synchronization in the WAAD sync tool, see this piece of documentation on TechNet.
The WAAD sync tool (version 1.0.6385.0012), that can be downloaded from your respective Office 365 Admin portal (direct link here: http://go.microsoft.com/fwlink/?LinkID=278924) supports this feature, so you can go test this right away!