Jackson is your rival. You encounter him for the first time in Pallet Town when you try to catch his Eevee. You will encounter him several times during your adventure.
You will encounter him in Pallet Town after trying to catch his Eevee. Defeating him is necessary to leave the town.
You will encounter him in Viridian City in the basement of the trainer school.
You will encounter him in S.S. Anne in Vermilion City.
You will encounter him in Rocket Hideout in Celadon City.