The point of Baker's boxes and clouds is to describe, for a particular system/procedure of play, the relationship between cues (like dice rolls, or charts, or PC sheets, or some mathematical operation) and imagined stuff ("the fiction"). (The "boxes" - dice - represent cues; the clouds represent imagined stuff.)
The basic idea of "fiction first" is to establish rightward arrows - ie from fiction to cues - rather than to have only leftward arrows, or recursive arrows from cues to cues. (
Here is where Baker uses the analysis to diagnose why his system In A Wicked Age is experienced as unsatisfactory by some RPGers.)
An example of a recursive arrow from cues to cues is "Roll to hit." => dice are rolled, final to hit number calculated using appropriate mathematical procedure => "OK, as per the stat block the AC is <whatever> and so that hits. Roll damage." => dice are rolled, final damage result is calculated using appropriate mathematical procedure => "OK, I've subtracted that number from the hit point number. It's now equal to zero."
There was one leftward arrow there: when the GM said "so that hits", that is, the mechanical process requires us to imagine, as part of the fiction, the attacking character doing <something or other> to set back their foe.
The final bit, about the foe's hit points being reduced to zero, is also apt to prompt the GM to say "They're dead!" which generates another leftward arrow - as part of the shared fiction we are now all to imagine that this being is dead, killed by the attacking character.
D&D combat often includes quite a bit of this sort of thing - lots of recursive arrows from cues to cues, the occasional leftward arrow (some not very crisp in terms of the imagination they produce like, "that hits"), and few or no rightward arrows. (There was no rightward arrow in my example, but presumably one occurred prior to the instruction to roll to hit: the player saying "I attack the foe", which is an event in the fiction that prompts the call to roll the d20.)
(For the curious, I've just reiterated Baker's steps 2, 4, 5, 6 from his Resolution System #1 on the blog I linked to above.)
A fiction-first system tries to increase the ratio of (i)rightward arrows to (ii) leftward arrows and recursive arrows from cues-to-cues.