In Pokemon FireRed and Pokemon LeafGreen, you get badges for defeating Gym Leaders, just like in any other Pokemon game. However, upon receiving the badges, it sometimes tells you that a stat of all of your Pokemon has been raised. Supposedly, the Boulder Badge gives raises your Pokemon's Attack, the Thunder Badge raises your Pokemon's Speed, the Soul Badge raises your Pokemon's Defense, and the Volcano Badge raises your Pokemon's Special Attack and Special Defense.
Additionally, according to Bulbapedia, the respective gyms in the Johto and Hoenn regions also give your Pokemon the same benefits (1st badge increases Attack, 3rd badge increases Speed, etc). However, I don't believe this is mentioned in-game.
I'm curious as to if these badges actually do raise the stats of your Pokemon. If so, by what value?