The answer is quite simple
The end result of a tic tac toe (or Xs and Os, Noughts/Knaughts and Crosses, etc. See; http://en.m.wikipedia.org/wiki/Tic-tac-toe#English_names) game.
Why?
A paper pound of wrong and round,
The game is played on paper with Xs (wrong) and Os (round). Pound having to do with # which is the shape of a tic tac toe board.
A minty piggy named.
A tic tac is minty. Then there's piggy toe!
Dividing nine, some yours, some mine,
The game is split us into 9 slots. Some slots are owned by you, some by your friend, Xs and Os!
A syzygy is claimed.
In astronomy a syzygy is the alignment of 3 celestial bodies! In other words, 3 in a row is achieved, or a "tic-tac-toe" Win!
*One note [POSSIBLE SPOILER];
Games can end in ties, so the last line is arguably correct.