From The Collaborative International Dictionary of English v.0.48 :
Latchstring \Latch"string`\, n.
A string for raising the latch of a door by a person outside.
It is fastened to the latch and passed through a hole above
it in the door.
[1913 Webster]
To find the latchstring out, to meet with hospitality; to
be welcome. (Intrusion is prevented by drawing in the
latchstring.) [Colloq. U.S.]
[1913 Webster]
From WordNet (r) 2.0 :
latchstring
n : opener consisting of a string that can be passed through a
hole in a door for raising the latch from outside