It means a lot to many a fathead (4)
I believe the answer is:
mass
'it means a lot' is the definition.
The definition suggests a singular noun which matches the answer.
'many a fathead' is the wordplay.
'many' becomes 'm' (Roman numeral for a thousand).
'a fathead' becomes 'ass' (I've seen this in another clue).
'm'+'ass'='MASS'
'to' acts as a link.
Can you help me to learn more?
(Other definitions for mass that I've seen before include "Widespread" , "Roman Catholic service" , "Religious rite" , "Body of matter" , "Throng" .)