Begin to understand material one doesn't finish (6,2)
I believe the answer is:
cotton on
'begin to understand' is the definition.
(I've seen this before)
'material one doesn't finish' is the wordplay.
'material' becomes 'cotton' (cotton is a kind of material).
'doesn't finish' means to remove the last letter.
'one' with its final letter taken off is 'on'.
'cotton'+'on'='COTTON ON'
(Other definitions for cotton on that I've seen before include "Perceive the meaning (of)" , "Understand (slang)" , "Begin to understand (colloq.)" , "Come to understand" , "In thin shirt" .)