Sudden awareness no great importance attaches to cry that floats up (5-4,6)

'sudden awareness' is the definition.
(term for suddenly understanding something)

'no great importance attaches to cry that floats up' is the wordplay.
'no great' becomes 'light' (light can mean trivial or unimportant, not great).
'importance' becomes 'moment' (moment is a kind of importance).
'attaches to' says to put letters next to each other.
'cry' becomes 'blub' (I've seen this before).
'that floats up' is a reversal indicator (in a down clue, letters go up).
'blub' back-to-front is 'bulb'.
'moment' after 'bulb' is 'bulbmoment'.
'light'+'bulbmoment'='LIGHT-BULB MOMENT'