In this example it means I really like her. It’s mainly used in the UK :)

fancy as a transitive verb, example "I fancy her" means like, am attracted to.

It is an interesting question because the meaning of 'fancy' is different in the US and British. In the US is posh, flashy In GB is to like someone

In this context, the term refers to attraction as in "I really like her". As far as I know, it's something that's mainly used in British English.