External users can now use their business email address to authenticate when invited into a site collection. The Windows LiveID allows external users to associate their business email address (ex: user@contoso.com) to the LiveID system. Office 365 customers can invite their partners and clients to external sharing sites using their primary email account. If this email has been associated to the LiveID system, then the external user can sign in with their primary user name and password.
*This update will roll out to customers over the next several months. We expect that all customers will receive the update by May 2012.

Additional Information:
To learn more, please read the SharePoint blog SharePoint Online: Service Update
To learn more about how to use external sharing, go here for Office 365 for enterprises or here for Office 365 for professionals and small businesses
To associate a business email user name to the Live ID system, start at https://idsignup.live.com/, select “Use existing email address” and fill in the easy creation steps