This means a lot to many a mug (4)
I believe the answer is:
mass
'this means a lot' is the definition.
The answer and definition can be both acts as well as being singular nouns.
Perhaps there's an association between them I don't understand?
'many a mug' is the wordplay.
'many' becomes 'm' (Roman numeral for a thousand).
'a mug' becomes 'ass' (I've seen this before).
'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 "load" , "Substance; a service" , "Holy service" , "Get together" , "Body of matter" .)