The sight of the kingfisher awakens Brian to the idea that he, too, can attempt to catch and eat fish:
Sitting on one limb was a blue bird with a crest and sharp beak, a kingfisher—he thought of a picture he had seen once—which left the branch while he watched and dove into the water. It emerged a split part of a second later. In its mouth was a small fish, wiggling silver in the sun. It took the fish to a limb, juggled it twice, and swallowed it whole.
Of course, he thought. There were fish in the lake and they were food. And if a bird could do it...
This happens in Chapter 11. Up until this point, Brian has been eating small berries, which were tart and hard to chew, as well as eggs, which were unpleasantly greasy and oily.
He craves the kind of food he'd eaten regularly, thoughtlessly, at home: hot dogs at a cookout, turkey at a Thanksgiving dinner. It's clear that Brian craves more nutrition than his current strategies are yielding, and he'll need to learn to fish if he wants bigger portions of food with more protein.
You might wonder why it takes so long for Brian to realize that fish are a good source of food. Hasn't he been close to the lake this whole time? Yes. But don't judge him too harshly. He's never had to survive on his own before, and he's constantly dealing with problems--like the fruit that made him violently ill, and the porcupine that injures him.