Here are two good videos that provide a great overview of Office 365.The first video is 9 minutes and runs you through the Admin interface. Note the remote PowerShell administration capability from your on-premise PowerShell prompt: Connect-MSOLService.
There are other helpful PowerShell MSOLService commands illustrated here.
The second video is just under 15 minutes but it will be time well spent. It gives you a walk through the different Office 365 applications. Good for SharePoint guys to have a glance of Exchange and Lync online.