"Trammie," "tram," "Care Bear," or similar words are insults used to describe players who prefer the Trammel facet and other facets with its rules set. The term, originally, was used by players who prefer Felucca, but has since achieved a somewhat broader acceptance, even being used by some Trammel players who describe themselves as "Trammies." (Though typically it retains its insulting connotation.)
Like other, similar terms, such as "twink" and "noob," "Trammie" has been long divorced from any particular, specialized meaning, and is often used as a generic insult. Players who you beat in PvP, or who beats you in a manner of which you disapprove, or who does not handle themselves properly in the dungeon Doom, have all been variously described as "Trammies."
Fellie, the equivalent term, is used far less and is of far more recent vintage.