The Long Walk is when a Judge leaves the city for the Cursed Earth or the Undercity to "bring law to the lawless".
Some aging Judges choose the Long Walk because they no longer meet the physical requirements to patrol Mega City One as a Street Judge, but cannot imagine themselves retiring to a desk job or teaching post at the Academy of Law. Other Judges might take the Long Walk if they have been somehow disgraced or disillusioned. Judge Dredd once took the Long Walk because he grew disillusioned with the way the Justice Department was doing things.
The Long Walk begins with a ceremony where the retiring Judge receives a gun salute by his comrades.
In the 1995 film, the Long Walk is mandatory for all Judges upon retirement.