The dictionary first gives this definition no. 3:
"3 (sometimes disapproving) expensive or connected with an expensive way of life"
and then use this example to illustrate this meaning or definition:
"Don't come back with any fancy ideas."
So "fancy ideas" here means expensive ideas or ideas connected with an expensive way of life.
On that basis, let me construct another example:
She has left her previous boyfriend, who was a poor artist, to be with a billionaire, who gives her fancy gifts from Cartier and takes her on fancy holidays by private jet.
That is how I would use the dictionary. Does this help you at all?