I admit this is a little difficult to grasp from the rulebook. But it is there.
Looks like you are playing Rise of the Runelords (based on the character and the blessing). I will note here that the governing rulebook is the latest rulebook, but even so:
Anyone can play a card whenever the card allows it.
So: in general, everyone can always play cards, even when it is not their turn.
Still:
You may not activate a power or play a card that doesn’t apply to your current situation.
(The RotR version lacks "or play a card", but the example immediately after indicates "power" is meant to include powers on cards; the language becomes more precise in the later rulebook.)
Also, during an encounter:
Characters may only play cards or use powers that relate to each step (or relate to cards played or powers used in that step). Each character may play no more than 1 card of each type during each step; for example, a character may play no more than 1 blessing while attempting a check, though multiple characters could each play 1 blessing.
So, during an encounter, the card has to relate to the step or check, and any each character can only play 1 card of each type.
Looking at Blessing of the Gods:
Discard this card to add 1 die to a check.
If a card says it effects "a check", or "any check", then you can play it for any character's check.
If the card says "a check at your location", then the character you play it on has to be at your location.If the card says "your check", then you can only play it to help you.
I feel I should add Runelords has a "gotcha" that has been mostly cleared up in later editions....
Note this rule:
No One Else Can Take Your Turn for You. Whenever you encounter a card or make a check, you—and only you—must resolve it. No other character can evade it, defeat it, acquire it, close it, decide what to do with it, or fail at doing any of those things.
Now look at a card like Thieves Tools:
Discard this card to defeat a barrier whose highest difficulty to defeat is 11 or lower.
You might think you could play this to defeat a barrier encountered by any character (at any location, in fact). You'd be wrong. Only the character who encounters the barrier could play Thieves' Tools to defeat it -- because no one can defeat a card a character encounters, except that character.
Cards that defeat or evade a card can't be played on other character's encounters, unless they explicitly say they can (like Sanctuary).
(Note: in later sets/class decks/promos, characters have powers that let them give or take encounters from other characters -- that's just an example of a card overriding the rulebook.)