Ykhjuy

I have read a few non-fiction works (mostly scientific) where there is a quote at the beginning of each new chapter. Sometimes the quote related to the chapter along with the title, sometimes it was difficult to make out why its there.

I am assuming this is to set-up a mood for the chapter or even summarize.

I had followed the suite for my novel. For an e.g. for the chapter where my MC recovers from divorce and starts a new life I have put the following quote at the start of the chapter. This quote I selected after googling quotes, I don't know much about the author but the quote suggests that she will recover in this chapter.

Her fetters burst, and just released from prison,
A virgin phoenix from her ashes risen. - Christiana Baldwin

Is this advisable for fiction novels?

A quote (called an epigraph) is added to the start of a book or a chapter when it adds an insight to the story. What kind of insight is up to you: it might be an additional understanding of events on a meta level, it can be foreshadowing, it can be extra information, etc. It is never a random quote found in google, since that adds no insight. The epigraph is as integral a part of the story you're writing as anything else. If it adds nothing, it shouldn't be there at all.

For example, Ernest Hemingway's For Whom the Bell Tolls starts with a quotation from John Donne:

No man is an Iland, intire of it selfe; every man is a peece of the Continent, a part of the maine; if a clod bee washed away by the Sea, Europe is the lesse, as well as if a Promontorie were, as well as if a Mannor of they friends or of thine owne were; any mans death diminishes me, because I am involved in Mankinde; And therefore never send to know for whom the bell tolls; It tolls for thee.

This epigraph should inform the reader's understanding of Hemingway's novel, convey that it is bigger than the story of one guy named Robert Jordan.

The theory of intertextuality assumes that all works of art are created within the artistic tradition or discourse and refer to preceding works or art.

One aspect of this is sometimes called "inspiration", where one artist feels inspired to create a piece of art by another artwork. But intertextuality goes beyond inspiration in that it encompasses "schools" of artists addressing similar topics or using similar styles and many other phenomena of similarities and relations between "texts" (where "text" is anything using a set of rules to express information, so a film or painting is also a "text" in this sense).

The epigraphs that you ask about are a way for an author to make explicit the connections to other texts that he wants to encourage the reader to consider in their reading.

But epigraphs have also become a fad so you might want to avoid them, especially if you aren't completely sure about how to use them.