To shake hands and mingle with many people, especially while campaigning for public office.
Political slang refers to handshaking during a campaign.
One could "press flesh" as candidate or on behalf of candidate or on behalf of political cause intending to garner support from those whose flesh is being
pressed.
Shaking hands while attempting
To exert
force or pressure.
To weigh heavily, as on the mind of another.
To advance eagerly; push forward.
To require haste; be urgent.
To assemble closely and in large numbers; crowd.
To employ urgent persuasion or entreaty.
To encourage (a falcon, for example) to participate in the
chase by feeding it flesh from a
kill.
Middle English pressen, from Old
French presser, from Latin pressre, frequentative of premere, to press. -Press
Middle English, from Old English -flesh