The Accelerated Dragon allows Black to adopt a Dragon setup without having to fear the Yugoslav Attack. By playing g6 earlier (usually in the line 1. e4 c5 2. Nf3 Nc6 3. d4 cxd4 4. Nxd4 g6), Black retains the ability to play d5 in just one move (rather than having previously played d6 in the standard Dragon), saving a tempo.
Conversely, this setup allows White to play the Maroczy Bind (5. c4), making this opening a much more positional one than the standard Sicilian Dragon.
If Black really wants to play g6 as soon as possible, an even faster way is the Hyper-Accelerated Dragon, where black plays g6 on the second move (1. e4 c5 2. Nf3 g6).