Quick Definition: When a PUA walks around introducing himself in a friendly manner, similar to a Mayor of a small town.
Mayor walking is a technique that PUAs use to get into social state and to build their social confidence. By walking around talking to everyone that he comes across, a PUA forces himself to get into a social mode and gets used to approaching and talking to strangers. PUAs also use mayor walking to short set venues in order to get into state and build social proof.
Mayor walking is an especially valuable exercise for newer PUAs who may be uncomfortable talking to strangers. Newbies can use the concept of mayor walking to put themselves in the role of the Mayor of their block and talk to anyone that they come across on their block, regardless of who they are. They can then gradually expand their “territory” to include their entire neighborhood, their workplace, their favorite bar, etc. until they feel comfortable striking up conversations with anybody, anywhere.
Source: Paul Janka