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In order to use your domain with Office 365, you will need to first verify your domain name, and then setup the DNS records that Microsoft specifies.
Step 1: Gather the Domain Information First you will need to obtain some basic information so that you can create the DNS record necessary for verifying your domain.
It is possible to use various services such as Microsoft's Outlook Web App through Office 365 with your own domain name while having Host Gator host your website.
Microsoft offers a product called Office 365, which provides many services such as web based email accounts.Once the required DNS changes have been made, it can take 4 to 8 hours for those changes to propagate (or update) worldwide.