Office 365 is the name of Microsoft's online services division. To install Office 2016 software on your computer, you need an Office 365 account. In other words, you must be a paid subscriber to Office 365.
As of this writing, a subscription to the Home edition of Office 365 costs $99.99 per year or $9.99 per month (Microsoft also offers a Business edition and University edition). An Office 365 subscription entitles you to these goodies:
The opportunity to install Office 2016 on five computers.
The opportunity to install Word, Excel, and PowerPoint on five iPads and/or Windows tablets.
Automatic updates to the Office software on your computer. As long as your subscription is paid up, Microsoft updates the Office software automatically.
The opportunity to store files on OneDrive, Microsoft's cloud service. In computer jargon, the cloud is the name for servers on the Internet where individuals can store files. Rather than keep files on your computer, you can keep them on the Internet so that you can open them wherever your travels take you. Subscribers to Office 365 get an unlimited amount of storage space on OneDrive.
The opportunity to use Office Online, the online versions of Word, Excel, PowerPoint, OneNote, and Outlook. To use an Office Online program, you open it in a browser and give commands through the browser window. Office Online software is useful for co-editing and sharing files.
To find out all there is to know about Office 365, visit this website.