Might as well take this off the unanswered list.
Thick Grass (also called Double or Dark Grass) is Grass in the overworld that is darker in appearance. You can encounter Double Wild battles here. Pokémon in this area are usually higher level than other Pokémon on the route. Your success in capturing Pokémon in this area depends on how many Pokémon you have registered in your Pokédex.
I cannot find much information on this. The information from the sources provided states the same thing as Thick Grass: The less Pokémon you have registered in your Pokédex, the harder it is to catch Pokémon in Mystery Terrain.
So, all in all, in the mystery terrain, it is extremely difficult to catch Pokémon at the beginning of the game, when you've caught few Pokémon, and it only becomes as easy as normal when you have more than 600 Pokémon caught.
I recommend giving the sources a good read, they're pretty interesting.