Hoenn is special because it's the best region ever.
First of all, Emerald was my first Pokémon game, so I am very biased in answering this question, but ignore that.
Hoenn is one of the most popular Pokémon regions, along with Sinnoh and Unova. These three regions have good reason for being the most popular. The all have good variety, good design, good music. It also helps that the games in which these regions were introduced are all great, with great gameplay, great plot, and great characters, as well as great Pokémon designs. Most fans think that Pokémon peaked somewhere between Gen 3 and Gen 5, and those regions happen to be the most popular.
I know for a fact that not everyone likes Hoenn (7.8/10, too much water) but it is certainly a good region. There are several things that make Hoenn special:
First, Hoenn has good design. There is so much variety, that it never get boring. Even though it's smaller when compared to other regions, Hoenn looks great. Each area has a theme, and the NPCs and Pokémon there echo this theme as well. Hoenn was Game Freak's first attempt at true worldbuilding, and everything just fits together.
Second, Hoenn has good music. If you are a fan of trumpets, this is the region for you. The music isn't outstanding or anything, it just fits with the region. Junichi Masuda did an amazing job making the music for this game. The music just blends very well together, and the similarities they all share (trumpets) makes it seem like the music is meant to be together. It doesn't feel like the music is just thrown in on top, it seems like a part of the game.
Third, Hoenn has good gameplay. This is the region that introduced Abilities and Double Battles, as well as the modern IV/EV system, all core mechanics that have stayed with the series since while other battle gimmicks/gimmick battles have faded away. (Triple battles, Sky battles, etc) The game is pretty well balanced, and there are no truly OP Pokémon that outshine the others. The starter trio is well balanced as well, with the worst one (Treeko) having a type advantage over much of this water-based region, to balanced the fact that it has the worst movepool and stat distribution of the three. The developers learned their lesson from Jotho, because the level curve in this game is very good. It's enough the keep you on your toes, but there are no spots where you truly have to grind. You have just enough exp to get where you need to be, without being overleveled.
Fourth, Hoenn has a good story and lore. The plot is great, with two evil teams instead of one, great characters, and it gives you a little bit of plot at a time to avoid huge infodumps. I'm not trying to say that it has an outstanding story, like the Unova games, but it has enough to remind you why you're playing. Overall, Hoenn has a good story about the limitations of humans, and what happens when you try to play god. Also, it has the first true cutscene in a Pokemon game, and a pretty epic one at that.
The Lore of Hoenn and it's legendries is also interesting. The Weather Trio, Groudon, Kyogre, and Rayquaza have a reason why they are a trio, Groudon and Kyogre fight for dominion of Hoenn, and Rayquaza tells them to shut up and go to their rooms. Deoxys, Jirachi, the Eon Duo, and the Regis all have great lore.
Fifth, Hoenn has good Pokémon, and that's kind of important because it's a Pokémon game. All the designs are great, even though they usually don't have that stats to back it up. Hoenn also throws some Kanto and Jotho Pokémon into the mix, to make it seem like it's a part of the Pokémon universe, and not isolated. Also, some of the obscure Jotho Pokémon are used like, Skarmory, Magcargo, and Xatu, making some people think that these Pokémon originated in Hoenn.
Sixth, Hoenn has good characters. There are so many, but I won't list them all. The characters have more depth then the ones from Kanto/Jotho. The Evil Team's leaders have more understandable motives, not just "I'm evil because I am evil", and they belive they are working for the good of Hoenn. Also, Hoenn has the first non-jerk rival, in Brendan/May. It's especially nice that Brendan and May are different, not just the same rival palette-swapped depending on your character choice. They even have different themes.
In summary, Hoenn has a lot of things going for it, and it deserves to be one of the most popular regions. I know this has been kind of a rant on how great Hoenn is, but none of the other answers actually answered the question of "What is so special about Hoenn". This has turned out to be very long, so...
TL,DR:
Hoenn is popular, and apparently there is a reason for that.
Hope I helped.
