Dances with a wife - that's a puzzle (6)
I believe the answer is:
jigsaw
'that's a puzzle' is the definition.
(jigsaw puzzle is a type of puzzle)
'dances with a wife' is the wordplay.
'dances' becomes 'jigs' (jigging is a kind of dancing).
'with' means one lot of letters go next to another.
'wife' becomes 'w' (abbreviation).
'jigs'+'a'+'w'='JIGSAW'
(Other definitions for jigsaw that I've seen before include "Puzzle with pieces to assemble" , "Problem with fitting in" , "Puzzle - powered cutter" , "Sharp tool (for cutting puzzle into pieces?)" , "Puzzle-maker" .)