The fate value on a stronghold determines the fate production of a player.
Both stats are represented by a cherry blossom icon. The production value is proceeded by a "+".
Fate is represented with small tokens placed in a pool for spending on card effects or placed directly on character cards as they are played onto the field to keep them available for multiple turns.
"At the beginning of the game, a card from the top of your dynasty deck is placed on top of each of the four province cards between your decks, while the fifth province hosts your stronghold. As the round begins, the dynasty cards on your four central provinces are turned face-up, and during the dynasty phase, you and your opponent will take turns playing characters from your provinces. All characters have a cost, shown in the upper-left corner, that must be paid in fate—a currency that represents the karma and destiny that a clan has accrued. There is an additional cost, however, that must be considered.
In Rokugani culture, a central philosophical concept is mono no aware. Literally translating to 'the pathos of things,' mono no aware is an understanding and bittersweet acceptance that everything in the world is impermanent and transient. In Legend of the Five Rings: The Card Game, this is played out through your characters and your fate. After playing a character from one of your provinces, you may choose to pay any number of additional fate, placing these fate tokens directly onto the character.
For instance, you may choose to play the Matsu Berserker from a province, paying one fate, as shown above. Considering your options, you decide that you will want this character in play for several rounds, so you place two more fate from your supply onto this character. At the end of this round, one of those fate tokens will be removed from the Matsu Berserker. If you had chosen to not place any additional fate on the Matsu Berserker, this character would have been discarded in this round's fate phase—the Matsu Berserker will have fulfilled their destiny at this point in the ongoing narrative of your game.
By placing additional fate tokens on a character, you are, in essence, paying to keep that character in play for additional rounds. Choosing exactly how much fate to invest in a character is a key strategic decision! If you don't pay enough, you could find your best characters have fulfilled their destiny and departed just when you need them most. If you pay too much, however, you may have bound your clan's destiny to a single character—which could leave you vulnerable to attacks on multiple fronts. Compounding the decision is the fact that you'll need to save some fate if you're going to play conflict cards from your hand later in the round. The clans gain more fate at the beginning of each new round, but deciding how to use your fate is crucial to victory."
What we do know is that the amount of fate generated each turn is primarily determined by each player's Stronghold of choice for their deck. This means different clans will likely have different options for how much fate they generate and how they use fate to play.
"A clan's stronghold is the seat of its power, providing your supply of fate, determining your starting honor, and offering a powerful ability that can be used throughout the game." 
The Fate Phase
The Fate Phase — Unlike in the Legend of the Five Rings CCG, your characters no longer remain in play indefinitely (unless removed by a card effect). Instead, when you play a character from your province or your conflict hand, you may choose to place any number of additional fate tokens on it from your supply of fate. During the fate phase at the end of each round, one of these fate tokens will be removed, or, if the character has no fate tokens, the character will be discarded. (For more information on the fate phase, read the "Embrace Your Fate" section further up on this page.