The Windows Insider Program is an optional service provided by Microsoft to let users experience the next version of Windows before public release. The program is aimed at early adopters and the 'enthusiast' crowd who enjoy beta testing new software. Besides just using the software, Microsoft encourages testers to send feedback on their experience through a specialized app, which includes ratings and a place to leave notes to the Windows development team.
The Insider Program was announced on September 30, 2014 during Microsoft's Windows 10 reveal. The initial release of Windows 10 through the Insider Program was aimed at enterprise users, although anyone can download the OS to their machine without cost. Since its release, Microsoft has pushed out various updates to Windows 10, bringing new features and fixes along the way.
On January 21, 2015, Microsoft is expected to announce an expansion of the program for consumers, including a version for Windows Phone. In early January, a new app from Microsoft called Phone Insider was released to the Store in anticipation of the announcement.
It is not yet clear if Phone Insider replaces Preview for Developers, a similar program that let consumers download the latest version of the Windows Phone operating system before carrier approval. Phone Insider is presumably a service for beta testing pre-release software, whereas Preview for Developers were finalized branches of the OS for public release.
More information about the Insider Program can be found at Microsoft's site dedicated to the service: https://insider.windows.com/en-us/