Girl grabbing boy's heart shows intention (4)
I believe the answer is:
goal
'intention' is the definition.
(I know that intention can be written as goal)
'girl grabbing boy's heart' is the wordplay.
'girl' becomes 'gal' (synonyms).
'grabbing' means one lot of letters goes inside another.
'heart' means to look at the middle letters.
The centre of 'boy' is 'o'.
'gal' going around 'o' is 'GOAL'.
'shows' acts as a link.
(Other definitions for goal that I've seen before include "Target or ambition" , "End" , "Football score" , "Aim and objective" , "A score in soccer" .)