You'll trigger this quest once you push Jodi to four hearts' worth of affection. After you do you'll get a little cut scene outside your house the next day, and Jodi will ask you to come to dinner at 7 pm. All she wants is that you bring a Largemouth Bass with you.
Largemouth Bass are somewhat elusive, but they're not too hard to catch. You can find a Bass at the lake near the Mines, in the northeast of Stardew Valley. They're appreciably wriggly fish, and you might have a bit of trouble catching one below a Fishing Skill of three or four. Bait will make landing one of these fish much easier.
Take your Bass over to Jodi's house once you have it in hand, entering her home at 7 pm. This will trigger a cut scene that will end the quest. I have no idea what this accomplishes, but I assume it provides a boost to affection with Jodi.