I caught a tremendous fish
and held him beside the boat
half out of water, with my hook
fast in a corner of his mouth.

These lines establish setting and subject. The speaker is fishing from a boat and has caught one of those fish that anglers dream about: it is "tremendous."

He didn’t fight.
He hadn’t fought at all.

Fish fight when they are being reeled in. The will to live and not be captured is wired into their survival. But this fish has not. He has resigned himself to whatever comes next, likely due to his experience seen later in the poem. The speaker notes near the end that

from his lower lip
—if you could call it a lip
grim, wet, and weaponlike,
hung five old pieces of fish-line,
or four and a wire leader
with the swivel still attached,
with all their five big hooks
grown firmly in his mouth.

This fish has lots of experience in being captured. At least five times prior to this, he has found himself hooked and has managed to escape. All five of these hooks are "grown firmly in his mouth," indicating that he has worn them for a long time. In the past, perhaps he had the youth and strength to fight against the one who sought to capture him. Now, however, he is old and resigned:

Here and there
his brown skin hung in strips
like ancient wallpaper . . .

The fish's physical appearance is noted to reflect his age. His scales no longer cling firmly to his body; they are loose, reminding the speaker of the way old wallpaper begins to peel from the walls, its bright patterns diminished over time. He is covered in both barnacles and sea lice. He is not a pretty fish, but he is a survivor.

I stared and stared
and victory filled up
the little rented boat,
from the pool of bilge
where oil had spread a rainbow
around the rusted engine
to the bailer rusted orange,
the sun-cracked thwarts,
the oarlocks on their strings,
the gunnels—until everything
was rainbow, rainbow, rainbow!

The fish's former victories overcome the speaker, and the spirit of overcoming fills up her boat. She realizes that she cannot take the life of an old fish who has survived so much. He has not fought and won so many battles in his youth simply to be captured in his old age with his "medals" proclaiming his former victories. She also repeats the image of a rainbow, often signifying life and promise, as it spreads "around" multiple images of human machinery and impact (the engine, the bailer, and so on). It covers all, becoming "everything"—as if reconnecting the human realm to the animal one. This solidifies her decision:

And I left the fish go.