What is the significance of number 365 in Microsoft Office 365?

I found this answer will be useful for you: Microsoft Office 365 is a subscription-based service which offers access to various services and software built around the Microsoft Office platform.
It first included hosted versions of Exchange, Lync, SharePoint, Office Web Apps, along with access to the Microsoft Office 2010 desktop applications on the Enterprise plan.
With the release of Office 2013, Office 365 expanded to include new plans aimed at different types of businesses, along with a new plan aimed at home users.
After a beta testing process which began in October 2010, Office 365 was officially launched on June 28, 2011.
Some plans for Office 365 also include access to the current versions of the Office desktop applications for both Windows and OS X for the period of the subscription.
In the case of Office 2013 on Windows, it is installed using a "Click-to-Run" system which allows users to begin using the applications almost instantaneously whilst files are streamed in the background.
Updates to the software are installed automatically, covering both security updates and major new versions of Office.
A feature known as "Office on Demand" is also available, which allows users to temporarily stream an Office 2013 application on any compatible computer without needing to fully install it.
All Office 365 plans are paid for on a subscription basis, monthly or annually.
"Microsoft Office" is the name we still use for our familiar productivity software.
Office suites have traditionally included applications such as Word, Excel, PowerPoint, and Outlook.
All the new Office suites (for example, Office Standard 2013) include the latest versions of these applications.
These suites can be installed on only one PC and do not come with any cloud-based services included in Office 365

"Office 365" refers to subscription plans that include access to Office applications plus other productivity services that are enabled over the Internet (cloud services), such as Lync web conferencing and Exchange Online hosted email for business, and additional online storage with SkyDrive and Skype world minutes for home.
Many Office 365 plans also include the desktop version of the latest Office applications, which users can install across multiple computers and devices.
The Office 365 plans that are online-only are a great choice for certain business needs, and they are compatible with desktop versions of the latest version of Office, Office 2010, Office 2007 (with slightly limited functionality), Office 2011 for Mac, and Office 2008 for Mac.
All Office 365 plans are paid for on a subscription basis, monthly or annually.
"Microsoft Office" is the name we still use for our familiar productivity software.
Office suites have traditionally included applications such as Word, Excel, PowerPoint, and Outlook.
All the new Office suites (for example, Office Standard 2013) include the latest versions of these applications.
These suites can be installed on only one PC and do not come with any cloud-based services included in Office 365.

That's the number of days in the year. Since Office365 is a cloud service, it's available365 days.

I am not familiar exactly the fundamental definition , significant of Ms Office 365 but I am get known that it is a subscription-based service which offers access to various services and software built around the Microsoft Office platform.

I exactly don't know but as the work of MS-Office 365 is then it might be the concept of sticking with this complete solution through out the year (which means 365 days).
You don't have to worry about anything else after signing to this version of MS-Office.
It's a subscription based system.
I am sure you must know all other provisions of this I should say "Online Community".