The part that hurt (3)
I believe the answer is:
bit
'the part' is the definition.
(both mean a piece of something)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for bit that I've seen before include "Unit of information" , "Segment" , "something boring" , "a curb?" , "Small piece; boring tool" .)