I will never understand what Groove Music is/was supposed to be. The Windows Media Player is still there and it's way more useful.
That's a long story that makes me sad.
In the early-mid 2000s, it became obvious to everyone that digital distribution of music was the future and the way to go. Yet the business model was unclear. For labels, it meant a problem because they were losing control of how music was getting into the hands of listeners. And there was piracy. Tech companies and manufacturers of various devices saw an opportunity and tried to enter the market. But labels didn't want to give provide this opportunity - they wanted control for themselves, without sharing any profits with those pesky bastards wearing jeans and t-shirts. And they worried about piracy, so there had to be some kind of DRM to protect the files. Various attempts were made to come up with a solution, and everybody wanted something that would give them control. Microsoft's first attempt was a cross-industry-wide DRM standard (I forgot what it was called), which was supposed to make sure that when you buy a song, it will play everywhere, and would be trusted by labels. That attempt failed miserably because neither OEMs nor labels wanted you to purchase a song a play it everywhere. OEMs wanted their own standards, and labels wanted to charge everyone differently through dozens or hundreds of small shady deals because that's how they like to operate, and because they hated tech industry.
So the whole thing was going nowhere, piracy was growing, everybody was losing, and then Apple came with this iTunes/iPod thingie. There was already a lot of demand for something like that and no supply. They obviously didn't have the OEM problem. How did they convince labels to cooperate? When Steve Jobs was asked the question, he said it was possible solely because they saw him as "one of them" because of his work at Disney. Yeah, it's that easy and stupid.
So Microsoft was frustrated but didn't give up, and came up with Zune. It bypassed the OEM problem and the door with labels was opened by Apple already. If you ask people who remember the name, they'll say Zune was a player. And herein lies the problem. It was a player AND a service, which everybody ignored. And it was an awesome service, let me tell you, I was one of the 12 people who used it. Microsoft couldn't compete with Apple in hardware and design really, so they decided to make something different in software, and they did. It was miles better than iTunes in three aspects. First, it had usable likes and dislikes, so it adapted gradually to your tastes in suggesting new music. Second, you could click an artist and were presented with a sort of tree view where you could follow who influenced this artist and who was influenced by this artist, thus going very far, crossing genre boundaries, which allowed finding some unexpected and interesting music. Third, monthly subscription gave you 10 DRM-free mp3s per month to download and keep forever. But, while the service was cool, it was more expensive than alternatives and you could only "get it" after using for a while, which of course meant that tech journalists didn't get it, and there was no single review that would show any hint of understanding of what the thing is about.
And that wasn't the only problem. In typical Microsoft fashion, it was developed by a separate team, and was competing with WMP as such. So it wasn't preinstalled, Zune player for PC didn't play videos, so you kind of had to have both anyway. It wasn't promoted by Windows in any way.
And that's how Groove came to be. Microsoft didn't want to leave the idea yet, so they decided to fix Zune's problems. Marketing folks said the brand was dead, so they renamed it. Somebody said the service was expensive, so they made it cheaper, but with the price drop they dropped features, too (the 10 downloadable mp3s were gone). Somebody said multiple players were confusing, so they decided to make one, and Groove Music came to be, but it didn't replace WMP completely (power user complaints), and the "influence tree" was gone, too. So it became a service indistinguishable from any other service. And then they decided that they can't keep losing money on it forever, so cost cutting started, and some label deals disappeared, selection deteriorated. At the end they just sold their user base to Spotify and closed the service, but the player remained.