The story really begins with the Xbox 360. Microsoft got an entire year of a head start over their main competitor, the PlayStation 3, and the Xbox 360 was enormously successful almost from the start. The console did many things right, while the PS3 did many things wrong.
For one, being published an entire year later did certainly not help the PS3. It also didn't help that, unlike the Xbox 360, the console used a very exotic processor architecture that was very difficult for game engines to optimize for. It took a year or two after the launch of the console that the big game engines finally started to be able to take advantage of the unusual processor design, and games started really competing with the Xbox 360 in terms of performance. For quite many years the PS3 was seriously an underdog in the competition. Quite fortunately for Sony, however, it almost miraculously succeeded in catching up, and actually ended up selling almost as many units (about 80 million, compared to the about 84 million Xbox 360's.) These sales figures were probably helped quite a lot by the fact that the PS3 had a BluRay drive, making it, at the time, a surprisingly affordable BluRay player.
While the PS3 managed in the end to catch up with the Xbox 360 in terms of success, the latter led the race for years, and it can arguably be said that it kind of won said race by a small margin.
Maybe for this reason Microsoft became, perhaps, a bit too sure of themselves, and tried too much to "innovate" with their next-generation console, ie. the Xbox One. They made many, many mistakes that cost them quite a lot in popularity.
Firstly, Microsoft wanted the Kinect to be an integral part of the console (so much so that there would be no versions of the console without it; it would be a mandatory peripheral that comes with the console). They really, really tried to push the Kinect as part of the Xbox experience, and induce game developers to use it. However, both the pre-launch and post-launch audience reception of this idea was lackluster, to say the least. Gamers were not exactly thrilled, especially given that the Kinect would raise the price of the console by quite a lot (which it really did.)
Microsoft's second mistake was to announce that the Xbox One would need to be connected to the internet, and for the Kinect to be always connected and turned on, or else it would refuse to allow games to be played on it. This announcement received a ton of backlash, all the way from gamers to big name critics. The backlash was in fact so enormous that Microsoft reversed this policy prior to launch. This was probably a very smart move, but it didn't exactly help their or their console's reputation; the damage was already done, and only partially fixed.
Their third mistake was to announce that copies of games would be tied to single user accounts, which meant that you wouldn't be able to give a game you had bought to a friend, or to buy used games. Same thing: Enormous backlash, causing them to reverse the policy prior to launch, but damage to reputation already done, only partially fixed. In fact, Sony got some free points by riding on this, and announcing that the PS4 would not have any such limitations.
Their fourth mistake was to concentrate way too much on multimedia features, and too little on actual games. In fact, in their big pre-launch E3 conference, their entire presentation was about multimedia features (such as video streaming, online video rental, and so on and so forth), and almost no mention of actual video games. You know, the main reason that people actually buy video game consoles. Microsoft really tried to "innovate" too much with the Xbox One. But this didn't sit well with their audience, and the reception was, once again, quite lackluster.
The console itself, once released, did not have the best possible reception either. Not only was it slightly less efficient than the PS4, but it was amazingly bulky (resembling a big VCR from the 80's), and had an external power supply ("power brick") with its own fan... which is on all the time, when it's plugged into a wall; even if the console itself is in sleep mode. And it's quite noisy.
Immediately after launch, the PS4 sold like hotcakes (possibly breaking records on the fastest-selling console ever, after launch). The sales figures for the Xbox One were significantly more moderate. It didn't exactly help that the Xbox One was significantly more expensive, mainly due to the useless Kinect peripheral.
Credit where credit is due, Microsoft tried to learn from their mistakes and went into quite a damage control mode. Some time after launch (about a year or so), they announced a version of the console without the Kinect, which was significantly cheaper, bringing its price point to the same level as the PS4 (and even slightly cheaper). Of course this had the unfortunate consequence that many people who had bought the original version with the Kinect (because there was no alternative) felt a bit defrauded because the Kinect was not, after all, an essential component, and game developers are probably not going to make many games for it. But that was just a minor drawback.
Secondly, in their 2015 E3 conference presentation, their tone had shifted radically. Now their presentation was all about games, games, and more games. Nothing about the multimedia features, and no mention of the Kinect. This was exactly what the audience wanted. Unfortunately, two years too late. Another announcement was backwards compatibility with most Xbox 360 games. Great... except that once again it was two years too late. If this had been a feature right from launch, it would have probably boosted sales figures.
So now, finally, three years after launch, we get to their improved version of the console: The Xbox One S. The new version is significantly smaller in size (almost the same size, in volume, as the PS4, although maybe just slightly larger), has an internal power supply, and is slightly more efficient. And most curiously, it does not have a Kinect connection port at all. (A Kinect can still be connected to it, but it requires an expensive adapter. It's quite clear that Microsoft is not expecting anybody to actually want a Kinect with it.)
(Not pictured in the image: The power brick of the original version. Which is about a quarter of the size of the Xbox One S.)
The Xbox One S is, arguably, what the original Xbox One should have been from the very start.
It seems that Microsoft is constantly late to the party with this console generation. Things that should have been part of the initial release are coming years later. This is almost the exact reversal of their performance in the previous console generation, where they were the clear leaders for years.
Will the Xbox One S be enough to save the console, or is it too late? My bet is that it won't save it, especially since Microsoft has already hinted at their next console version. I don't think many people, especially those in the know, will want to purchase an Xbox One now, especially if they own a PS4 already. (Some people who don't have either, and really want the Xbox, eg. because of brand loyalty, might now be induced to buy the S version, but I'm betting these people are quite a small minority.)
Edit 8.8.2016: Anecdotal evidence is making the rounds that the Xbox One S is actually selling really well, at least on the initial days after release, with many stores being sold out. These are of course just unconfirmed rumors at this point, because no official sales figures have yet been released, but it seems that my prediction might turn out to be wrong. (It is, of course, also possible that even if the rumors are completely true, the sales will plummet after the initial rush.) I may make a new edit after more reliable figures come out.
