I'm speaking under correction (feel free to complain), but I think DirectX was primarily made to make developers leave DOS as a game's platform.
Many features of DirectX were related to multimedia and designed with the limits of Win95 in mind.
In the early years, the software render was the reference system.
Graphics cards were primarily 2D and supposed to assist drawing the output of DirectDraw&Direct3D.
Otherwise, GDI and the DIB engine were used as a fall-back for all the higher level APIs.
In the following years (or rather, months; the 90s were a fast lane), dedicated 3D hardware emerged.
Cap Bits in their drivers told DirectX what each of them were capable of.
Initially, they all were a bit behind the software render in terms of functionality (of Direct3D).
Water effects, reflections, fogs, surfaces, filtering.
But then, they quickly catched up both performance wise and in terms of features.
Eventually, they overtook Direct3D / the software render in terms of features.
This was approximately around the DirectX 6/7 era,
when games began to require or expect graphics cards with a certain feature set.
Windows 98 / DirectX 6.x was sort of in a limbo. IMHO.
It made full use of new 3D accelerator/graphics card features, such as bump-mapping ?,
but also simultaneously used MMX in order to compensate for the lack of specialized hardware.
With DirectX 7, things like Transform&Lighting (T&L) were introduced,
which wasn't available via the software render itself, but simulated via the 3D card's driver maybe.
Still, most DirectX 7 games did run on simple hardware.
DirectX 8/9 was going to make powerful hardware ubiquitous.
Shaders were introduced, with the dated software renderer/rasterizer not being able to emulate.
Despite this problem, most entry-level hardware (notebooks) was stuck at the v8.1 level, sadly.
If the hardware was too old, games didn't even start. Not even with reduced visuals.
In short, the whole game industry peed on your doormat. No fancy hardware, no fun.
Personally, this was the time when I stopped caring about video games, except for new indie games.
Ironically, these often used the more modest Direct3D 3/5/6 and/or OpenGL 1.x often. Or DirectX 8.x, if they were more sophisticated (say, The White Chamber/Wintermute engine).
And GDI/DirectDraw, if they were 2D.
After the DirectX 9 years, DirectX 10 was introduced with Windows NT 6.0 aka the old maid. Big, slow, cumbersome..
Soon after, DirectX 10 was partially ported XP.
Unfortunately, most games still ran on DirectX 9 didn't really need or use DirectX 10.
Also because of the one and only Windows release it supported at the time (DirectX 10.1 added a few more useful things).
With DirectX 11, a fine feature was added: Tessellation.
For the first time, an elegant render method of high accuracy was introduced.
It was the most important update in the past years, perhaps.
DirectX 11 was backported to the old maid by The Platform Update, even.
Unfortunately, it was released somewhat late to save the old lady.
(The remaining Cap Bits were removed in the DirectX 10/11 era.
The WARP rasterizer was introduced. Mainly for drawing the Aero GUI on weak hardware ?
In this era, DirectX 9.0c was also implemented two ways;
as native, dedicated API and as Directx 9L aka 9EX at the side of DirectX 10/11)
Then, for many years that followed, nothing improved.
Microsoft didn't do anything meaningful for DirectX, the game industry was rather grumpy.
(Not as if that really mattered anyhow, considering the mediocre content. Remember Second Life?)
Up until AMD released Mantle, a fine little API, which blew Direct3D out of the water.
It was featured in many articles, even though only a handful of engines had support for it shoe-horned in at the time.
A few months later, Microsoft was urged to actively work on DirectX 12.
DirectX 11.1 re-introduced Cap Bits.
Real Raytracing, as it was known in the late 80s/early 90s CGI, also found its way into gaming in the 2010s.
It merely took overpowered graphics cards with the power draw of a fridge
and game engines with a few gigabytes in size to finally handle it.
Vulkan, as an API, was created from the ashes of Mantle.
To replace both Direct3D and OpenGL.
Architectural, it was capable of supporting old Windows XP, even. Unfortunately, no XP drivers with Vulkan were released anymore by graphics card makers.
On MacOS/iOS, Metal was introduced roughly the same time.
Edit: I'm focusing on the graphics part of DirectX here.
As it's name implies, Direct X (X=something, manyfold) has other features, too.
But I'll leave that out. Whenever I mention the audio parts, people seem to be unhappy with my listing.
Edit: Be ware of DirectInput DirectPlay. Never mention it. It's sort of a hot topic for game developers. 😁
Edited.