With Office 365, it is possible to invite external people to access your private SharePoint collections.
However, this feature is not enable by default.
So, to enable this feature, there are few actions to do.
First, connect to the SharePoint Administration portal (https://yourdomain-admin.sharepoint.com) and go to the Site Collection Management
Select the site collection on which you want to allow external user invitation and click on the Manage Share by Email button
Click on the Enable option
Then connect to your site collection and go to the Site Settings
Then click on the Site collection features link
Enable the feature External user invitations
Finally, open the Site Actions menu and click on Share Site
Enter external user email addresses on the field associated with the right level to provide to external user
A confirmation is shown if email invitation has been sent successfully
External user receive the invitation to access your SharePoint site
Once external user has accepted the invitation, it appears on the People and Groups list and no license has been consumed