The purpose of the notation is to show more clearly the different independent lines of the musical texture. By using three staves, we see more easily the bass/accompaniment voice in the bottom staff, a melodic line in the middle staff, and a shimmering texture in the upper staff.
As for playing it, it's typically up to the performer how to split this material up into two hands. Composers split them up in different ways, so choose what makes the most practical and musical sense for you, and feel free to change your approach as needed.
Notice, for instance, that the top staff has rests on the downbeats, and both outer staves have (non-notated) rests at the end of each measure. These are clues that suggest when hands are supposed to be playing material in other staves.
In many cases, one hand will be playing two staves; in other instances, a single staff will occasionally need to be split among both hands.