Uncovering the Accelerated Dragon opening I had previously heard and seen in commentaries about the Dragon opening where black plays an early g6 to develop the bishop on g7 after the typical open Sicilian starting moves c5 cxd d6. But how does the Accelerated Dragon differ from the usual Dragon and what aspect of it is being accelerated? 

A short explanation of the naming and summary of the underlying opening idea would really be helpful.
Dragon

The opening is named after the Draco (Latin for dragon) constellation because if you remove all the pieces and just look at black's pawn structure with the  pawns on g6 and d6 it looks like the dragon constellation as shown below (image source):





Accelerated

Unlike the mainline Dragon Sicilian where d6 is a key early move (1.e4 c5 2.Nf3 d6...), even though later it might still be pushed to d5, the accelerated version attempts to play d7-d5 in one go, without the inclusion of an early d6 move, and hence the name accelerated Dragon.

Here's an important move order that really typifies the accelerated Dragon, where everything black has set out to do has been achieved: safe king, healthy development, a successful early d5 push to undermine white's center, powerful bishop on the long diagonal, active play in the center and on the queenside. I highly encourage you to closely study the 3 variations that can result from either of the 3 ways white can capture the pawn on d5 on the next move.

 [Title "Accelerated Dragon, typical position"]
 [fen ""]
 [StartFlipped "1"]

 1. e4 c5 2. Nf3 Nc6 3. d4 cxd4 4. Nxd4 g6 5. Nc3 Bg7 6. Be3 Nf6 7. Bc4 O-O 8. Bb3 a5 9. f3 d5


Basic plan for black:

In short, having neutralized white's central d4 pawn for our c7 pawn, black fianchettoes their kingside bishop and exerts pressure on the long diagonal from the get-go, unlike most other Sicilian variations where the dark squared bishop stands quite defensively. Additionally, the fianchetto structure is a good defensive fortress for the king. 

Moreover, black's kept both central pawns (e and d) and in the future they can potentially make a better claim at central control as the central pawns are 2 for 1 in favour of black. Considering that white's only remaining central control lies in their e4 pawn, with constant threats of e5 kicking our knight to a less ideal  post, black's constantly playing towards making the d7-d5 break happen as early as possible, neutralizing white's only  central foothold.