The Enhanced Graphics Adapter (that's what EGA stands for) was a huge
step ahead from CGA. It was part and parcel of
IBM's new AT (Advanced Technology) in 1984, which also featured a 286
processor, a new keyboard with more function keys, a 16-bit bus, and
a 20MB hard drive, and a battery that enabled it to remember the time
and date even when turned off.
IBM had originally believed that most PCs would run only one program in their whole existence. Under this assumption, to have a seperate adapters and monitors for text mode and graphics made sense. But meanwhile experience had shown that the assumption was wrong, and so the Enhanced Graphics Adapter was a bit like an MDA and CGA rolled in one.
The horizontal resolution was reduced to 640 pixels, which didn't matter much, it just meant that there was only one column of pixels, not two, separating the characters. The vertical resolution stayed the same, 350 pixels. So now you had a text display in basically the same quality as the MDA, but with 16 colors.
But additionally, each of these 224,000 pixels could be addressed seperately, something the MDA had not allowed and consequently became the unique selling point of the Hercules adapter. The EGA had thus a hi-res graphics mode. What more, this graphic mode was not restricted to the traditional 16 IBM colors, the 16 colors could be chosen from a far larger palette.
The traditional IBM 16-color palette was based on the fact that there were four stages of intensity for red, green, and blue each. They could be completely off, full on or at one third or two third intensity. Now what do you get if you allow every possible combination of these intensity stages? You get a palette of 64 colors, and that was the palette of the Enhanced Graphics Adapter:

For a short while, the PC had the pole position as far as graphics were concerned. Unfortunately this palette was available only under the full resolution of 640×350. The old CGA resolutions (320×200 and 640×200) were still supported, could even show 16 colors at once, but only the old 16 IBM colors.
I'm listing only those modes I've seen used at least once.
This is the one mode where EGA showed its full power, these are the true EGA graphics. Unfortunately, it had two disadvantages:
So support from professional game programmers was always somewhat lackluster if it was there at all. Some games stretched 320×200 graphics to fit this mode to get the better palette, Blue Angel 69 for example, or Might & Magic III. In general, the 10h mode was used only in a few niches:
So far I found only one commercial American game can be said to have really used this mode, and that is Sea Rogue. SimCity doesn't count, by its nature it could utilize any resolution (and did, on the various platforms), and the graphics did not take the distortions of the resolution in account at all.
This is a rather obscure mode. The only game I know to have used it is Oxyd. Consequently I don't really know anything about it. Did it support the full EGA palette or only the 16 IBM colors? Could both colors be set or only the foreground color? I don't know.
Not an unattractive mode, but used very rarely, and then usually for ports of Japanese games, since this is a common mode on the NEC PC-88. Thexder, Sorcerian, Railroad Empire, Gemfire and all the other Koei strategy games used it. Not much else to say about it.
This is the mode that was used most often, so that it is often the
one that is identified with the term EGA.
Dh was mainly the
realm of commercial development, there are very few enthusiast games
that use it (The Battle on the Black Sea
and The Black Orb
are examples). There were lots of shareware games that used it, but they
were distributed by the big shareware vendors and obviously created with
the intent of making money.
While this mode was of course vastly inferior to the neglected 10h,
it could be used to create remarkable graphics. Outstanding examples
are P-47: Freedom Fighter
and Teenage Queen.
In both cases the artists understood that highlights and shadows do not
have to be the color of the object. There are only two shades of green
available, so P-47 uses yellow for the highlights and gray and black
for the shadows of the hills, and it looks very natural.
Other interesting examples are Sword of the Samurai; the tiles (but not the sprites and portraits) of The Keys to Maramon; the portraits from the Bard's Tale series and Wasteland. With a lot of games ported from the Atari ST and the Amiga however, the graphics lost a lot in the transition.
This is a pure legacy mode, it's the good old low resolution, 4 color mode from CGA. But under EGA, you could now freely choose the palette just as you could already choose the background color. This mode wasn't used very often, some examples I know are GJID, The Solar Hockey League, and Bob Winner. The palette could be changed without redrawing the screen.
Of course, it makes you kinda wonder why CGA didn't have this feature to begin with. I do assume it would have needed some added circuitry and thus have made the card more expensive, but the main cost factor at the time was video RAM, which would not have to be increased.
The only difference to CGA was the higher resolution and thus greater detail of the characters, something that is not necessarily an advantage for games, compare these Alphaman screenshots.
Mode Number Text Res. Graphics Res. Description Adapters Max. Pages
---------------------------------------------------------------------------
0h 40×25 ------ B&W Text CGA+ 8
1h 80×25 ------ B&W Text MDPA+ 8
2h 40×25 ------ Color Text CGA+ 4 or 8
3h 80×25 ------ Color Text (MDPA?)/CGA+ 4 or 8
4h 40×25 320×200 4 colors CGA+ 1
5h 40×25 320×200 2 colors CGA+ 1
6h 80×25 640×200 2 colors CGA+ 1
7h 80×25 ------ B&W MDPA (CGA+?) 1
8h to Ch -- PCjr or other adapters; no longer used
Dh 40×25 320×200 16 colors EGA+ 8
Eh 80×25 640×200 16 colors EGA+ 4
Fh 80×25 640×350 2 colors EGA+ 2
10h 80×25 640×350 16 colors EGA+ 2