Tiggy touchwood, a.k.a ticky touchwood, or simply touchwood, is an archaic form of tag.
Tiggy is an alternate form of the word tig, the old name for tag (incidentally, 'tiggy' is still used in Australia and New Zealand). Touch wood refers to touching wood. And there you have the game. One player is Tiggy (or Ticky, or It), and the others find a piece of wood to touch. The Tiggy recites a short verse and all players have to leave their piece of wood and find another; as they run, the Tiggy tries to tag them.
Tiggy, tiggy, touchwood,
My black hen,
She lays eggs for gentlemen.
Sometimes nine and sometimes ten,
Tiggy, tiggy, touchwood,
My black hen!
Rules vary, of course. The players have to decide what will count as wood (often branches, twigs, and trees don't count). Sometimes players have to declare when they reach a safe base, or can't go back and forth between two bases on sequential rounds. If obvious boundaries are not in place, they need to be defined. A touch-iron variant was apparently quite common as well.
It is quite possible that this game is where the phrase touch wood to ward off bad luck originates, although there is much debate on this.