Understanding it’s taking the public’s fancy (8,2)

'understanding' is the definition.
The definition and answer can be both related to thinking as well as being present participle verbs.
Perhaps you can see a link between them that I don't see?

'taking the public's fancy' is the wordplay.
I cannot really understand how this works, but
'taking' could be 'on' (eg one taking drugs is 'on' drugs) and 'on' is found within the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is present in the answer.
The remaining letters 'caching' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

'it's' is the link.

Can you help me to learn more?