The Orphan was invented by David L. Brown in the early 1970s.
Brown, who is a problemist, invented the Orphan for the purpose of using it in chess problems, for which it is very well suited. Brown's book, White and Black from Brown - A Selection of 168 Diagrams and Chess Related Fluff, contains many problems using the Orphan. One of Brown's Orphan demonstration problems appears below.
The standard symbol for the Orphan in problem diagrams is a circle.
In the diagram below, the black King is checkmated. If you're not sure why, an explanation is given below the diagram.
The white Orphan on d5 is attacked by the black Rook on d3, therefore
it gives check to the black King. Actually, it gives doublecheck,
since it attacks the black Orphan on a5, who in turn attacks the white
Orphan on a1, who attacks the black Orphan on h1, who attacks the
white Orphan on h2, who also checks the black King.
The black King has no squares it can move to, note that it can not
move to g4, because it would then attack the Orphan on f4, which would
check the black King.
Black can not play R:d5. If he did, the Rook would now attack the white
Orphan on d8. This would set up a new Orphan chain, d8-g8-h8, which
would check the black King. Therefore, R:d5 is illegal.
Likewise, Black can not play O(a5):d5 either. The black Orphan on d5 is
now attacked by the white Bishop on c4, which give Bishop power to the
white Orphan on f7, checking the black King.
And of course, moving the Rook on d3 along the third rank does not work,
since the Rook on d2 would then attack the Orphan on d5. Therefore,
Black has no way to get out of check, and is checkmated.
The Orphan's complimentary piece is the Friend, also invented by David Brown.
David Howe discusses the Orphan and Friend in a broader context in his article on Mimics.
Torsten Linss has three published problems using the Orphan, which he has online here.