If your Office 365 tenant has been migrated to the new 2013 experience, you may have noticed that there are 2 public web sites. The new one and the old one.
If you used the previous public web site, you may not want to build a whole new website from scratch on the new public site.
Thankfully, Microsoft is offering a free migration tool to move from the old public site (from SharePoint Online 2010) to the new one (on SharePoint Online 2013)
You can find more details here: