Unwanted, non-personal email received from a family member, friend or colleague.
Granny spam has usually been forwarded several times and concerns such inane topics as childish jokes, dubious political propaganda, spurious computer security alerts or claims of monetary recompense in exchange for forwarding of said spam.
Subject lines are often of the form "FW: FW: FW: FW: bullshit"
Origin: Usenet, circa 1990-1999.
'granny spam', ... it's the kind of thing your grandmother, who has just discovered this newfangled internets thing, is likely to forward.