First and foremost (IMHO), Microsoft wants to appeal to developers. They want their development stack to run anywhere there are developers. Notably, Microsoft just released Visual Studio 2017 for Mac on May 10th! Many developers out there run on non-Microsoft workstations, notably Apple computers. Apple’s OSX operating system is originally derived from the FreeBSD operating system. FreeBSD and other *BSD operating systems share much in common with Linux. So, if you can make SQL Server work on the Apple, you’ve probably made it work on Linux. Arguably, covering these two platforms nails just about every widely adopted development platform out there.
Microsoft also wants to appeal to a broader customer base, which means exploring the other environments that software runs on. An exceptionally high number of the world’s servers are powered by Linux. It’s lean, mean, stable, and powerful. Lots of shops refuse to run a Windows-based server because of a number of reasons, including that their in-house IT staff only have Linux knowledge. These same shops are most likely pressured to run a SQL Server for various applications. I know a number of third-party vended application that require a SQL Server, and previously if an organization dictated no Windows-based servers, that meant that this application would never be adopted in the organization, no matter how well it would function.
David provides a good explanation and sets up the context behind his upcoming SQL Server on Linux series.