A verbal marker is a perfect marker if it indicates that the event occurs prior to the topic time and its effects persist at topic time and if it cannot be used for a sequence of successive events in a narrative.
An alternative term is "anterior" (Bybee et al. 1994: 54).
Note that the persistence of effects is clearly noticeable with telic situations (because the result state must obtain at topic time), but not necessarily with atelic situations.
Note that I replaced "situation" by "event", because perfects are only defined for events (not states).
"Anteriors (or "perfects," as they are often called) differ from completives in being relational: an anterior signals that the situation occurs prior to reference time and is relevant to the situation at reference time. Anteriors are typically translated with the English perfect and often accompanied by the relational adverbs 'already' and 'just'. Anteriors may occur with past or future tense marking." (Bybee et al. 1994: 54)