It must be a Microsoft account or an existing Office 365 account.
Office 365 External Sharing
External Sharing in Office 365 enables an organization to extend
access to sites and site data with users that are not members of the
Office 365 subscription or do not have accounts within the source
Office 365 subscription. Individuals who do not have user accounts for
the source SharePoint Online environment are considered “external
users”. External users can be comprised of vendors or customers, for
example. Activating the external sharing feature in SharePoint Online
allows a site collection to invite external users to use the site
and/or site content through email-based invitation.
In Office 365 Enterprise plans, an organization can choose to manage
external sharing centrally through the SharePoint Online
Administration Center, enabling or disabling external sharing globally
or through specifying more granular sharing options such as allowing
sharing only with sign-in at the site collection level. Additionally
management of external sharing can be achieved through using Windows
PowerShell.
In Office 365 Small Business plans, the administration experience for
the management of external sharing is provided through a simplified
on/off switch within the Office 365 Service Settings.
External Sharing can be implemented in one of three ways when using
Office 365:
There are three ways that you can do this:
- You can share an entire site by inviting external users to sign in to your site using a Microsoft account or a Microsoft Office 365 user ID.
- You can share individual documents by inviting external users to sign
in to your site using a Microsoft account or a Microsoft Office 365 user ID.
- You can send users a guest link that they can use to view
individual documents on your site anonymously.
http://blogs.technet.com/b/wbaer/archive/2013/05/08/sharepoint-server-2013-extranet-and-office-365-external-sharing-considerations.aspx
You can send the email invitation to any email address, but to sign in, it has to be a Microsoft account or an Office 365 account.