Here's the explanation I found very intuitive from our mesoscopic physics class.

1. Edge states form because at the boundaries the effective potential for electrons goes to infinity – these are real "walls" on the edges. Electrons cannot move outside of the sample and therefore their wave functions are zero outside the walls. We have seen in very elementary quantum mechanics the "infinite square well" model and here you see it in action.
2. Since the potential shoots up to infinity, it must cross the chemical potential near the edges.
3. The electrons available for transport all reside at or close to the Fermi level. In the bulk, electrons are in the heavily degenerate Landau levels, which are usually some distance below $E_F$. The Fermi distribution means that all these Landau levels are usually fully occupied. Therefore there is simply no empty states for the electrons to go into in the bulk, even if they'd like to scatter to the center. Thus electron transport and current only occur along the edges.

All these can be found in Cees Harman's lecture notes on mesoscopic physics.

Here's the explanation I found very intuitive from our mesoscopic physics class.

1. Edge states form because at the boundaries the effective potential for electrons goes to infinity – these are real "walls" on the edges. Electrons cannot move outside of the sample and therefore their wave functions are zero outside the walls. We have seen in very elementary quantum mechanics the "infinite square well" model and here you see it in action.
2. Since the potential shoots up to infinity, it must cross the chemical potential somewhere near the edges.
3. The electrons available for transport all reside at or close to the Fermi level. In the bulk, electrons are in the heavily degenerate Landau levels, which are usually some distance below $E_F$. The Fermi distribution means that all these Landau levels are usually fully occupied. Therefore there is simply no empty states for the electrons to go into in the bulk, even if they'd like to scatter to the center. Thus electron transport and current only occur along the edges.

All these can be found in Cees Harman's lecture notes on mesoscopic physics.