In the 90's id Software was one of the most influential game developers in the world. If talking about the first-person shooter genre, arguably the most influential.
While Wolfenstein 3D was somewhat of a hit, perhaps no other game in history has had such a big impact and influence in video gaming than their next hit, Doom. This was the first-person shooter. Heck, for several years all subsequent first-person shooters by other companies were called "Doom clones". (The term slowly changed to "first-person shooter", but for quite many years "Doom clone" was in widespread use.)
Doom had many technological innovations unseen at the time, and it hit the market at the right time.
And that was one of the staples and defining characteristics of id Software: Innovation. Their games were always technologically ahead of most competitors, and they were essentially the leaders of first-person shooter gaming technology, while all other companies were followers and imitators.
That's not to say that other companies didn't make technological innovations of their own. Of course they did. It's just that for many years they lived in the shadow of Doom, and later Quake, from the gamers' perspective. (For example, the engine used in Duke Nukem 3D was technologically significantly more advanced than even the latest Doom game engine, yet it still had to live in the shadow of the latter, always being compared to Doom.)
Their next big hit was Quake, which also had significant technological innovations. While certainly not the first truly 3D game (ie. with free geometry, movement and orientation), it was in many ways the most advanced and, especially, most efficient game of that type for a time. By this time the term "Doom clone" had been pretty much phased out, but other first-person shooters were often now compared to Quake, and had to often live in its shadow.
Quake was initially fully software-rendered, but had an OpenGL port later. However, the first "properly" hardware-accelerated game by id Software was Quake 2. Again, it introduced a stock of technological innovations, which most other games and game engines had to catch up to.
At this point id Software was also a big name in terms of game engines. While not the only reusable game engine around, theirs was among the top most popular ones. Quite many games used the Doom, Quake and Quake 2 engines. By this time they had a big "feud" with the other biggest competitor, the Unreal Engine, but they were still one of the biggest.
However, something happened some time between Quake 2 and Quake 3 Arena. While the latter was a popular game, it had not such a huge innovator, nor was its engine such a huge hit. It wasn't anymore the first-person shooter that overshadowed all others, and to which other games were compared to. By this point other first-person shooters could stand on its own, rather than being compared to the latest one by id Software. In other words, id Software was not the "leader" anymore, just another competitor in par with everybody else.
Again, Doom 3 tried to innovate, and it did in many aspects, and it was somewhat of a hit... but somehow it didn't attain the same position as the first Doom did. Quake 4 went largely unnoticed.
By this point id Software's game engines had lost most of their market share. The big name was Unreal Engine, and some other smaller engines. Somehow id Software's engines had been relegated to almost obscurity, and almost no other company used them. Neither their games nor their game engines were the market leaders anymore; other companies had surpassed them by a landslide.
id Software next tried to innovate with their next game Rage. It certainly did have many innovations... but they mostly seemed hollow and unimportant. While many of the new innovations sounded good on paper, they didn't really make their actual game stand out from the rest of the contemporary games, technologically speaking. In fact, it didn't look any better than other games using more "traditional" existing technology. (In fact, in some aspects it even looked worse.) The game itself was also bland, and didn't have much success.
Only a handful of other games used its game engine. By this point Unreal Engine is the de facto first-person shooter game engine. The amount of games using Unreal Engine is staggering. Also other smaller engines had surpassed id Software's popularity, and by quite a lot (such as the Unity engine.)
Try as they might, it seems that id Software just can't regain their former glory, their former leader position, where everybody looked up to them, and everything else was compared to their games. Other game engines and games surpassed them, and went far ahead. Perhaps other companies understood what was practical about developing games and making them look good, rather than being so "innovative" with exotic new features.
At least id Software is still alive and kicking, but they are trying to catch up with the leaders, with very good efforts, but somehow failing. They just aren't the big name they used to be.