Hafez (1320-1389) is best known as a Sufi mystic who incorporated elements of Sufism into his verses.
A Faal is a practise of divination.

A فال fāl, s.f. An omen, augury, presage;—enchantment, spell:—fāl kholnā (-kī), To tell (one’s) fortune (by reference to his magical books,—a soothsayer); to foretell events; to practise augury
Calling it  Fortune telling or prediction would be a crude analogy. I think divination/omen is correct.

It is very popular in Iran where there are fail-e-Hafez cards which are very similar to tarot cards.

fal-e-Hafez

In the Persian tradition, one asks the Oracle of Shiraz for guidance when one is in two minds about future course of action and can’t decide what to do.

Hafez, in his own enigmatic way answers the seeker by guiding him / her through his verse by nudging them in right direction after looking into the mirror of their own soul.
Upon reflection in the mirror of Hafez’s Ghazal one would be inspired with an answer, a guidance or a direction.

These days I am studying the mysteries of Persian poetry with Prof Yunus Jaffery in the walled city of Shahjahanabad.
He was kind enough to show me how it’s done.

One recites a prayer
Ai Hafiz e Shirazi
Tu kaashif  har raazi
Tu ra qasam e shaakh  e nabood
Be guh har che hast raaz
Bismillah  ir Rahman or Raheem

And then with a calm and pure heart opens a page and pinpoints a verse.
The verse is then decoded to serve as an indication to you.

The verse I got was
Ayyam gul chu umr be raftan shitab kard
Saqi be daur e badah gulgu’n shatab kard

The days of the rose like life went in hurriedly

The cupbearer served a round of the rose coloured wine hurriedly

And I know I am in a hurry to do so many things and am trying to do them all at once !

I have miles to go before I sleep
And miles to go before I sleep