Dragon Ball's Master Roshi has picked up a couple of different names over the course of his life. He's most commonly known as the Turtle Hermit by those not familiar with him. However, he has one more identity that even those closest to him don't realize he ever went by -- Jackie Chun.
The Jackie Chun alias is an obvious reference to Jackie Chan, but there's a little more to it. In the anime, Master Roshi used the name and associated persona to fight in the World Martial Arts Tournament against Goku and Krillin. This seems odd at first, as he has no apparent reason to hide his identity, especially not from his own students. However, there's a reason for this roundabout method of competing, and it's a rather important one.
Master Roshi competed in the 21st and 22nd World Martial Arts Tournaments with the express purpose of beating his own students. With how powerful Goku and Krillin (and Yamcha) had become, they could easily beat just about anybody in the competition. If they were to beat everybody else and win, they'd be convinced that they were the strongest in the world and rest on their laurels.
From Master Roshi's point of view, the Tournament isn't meant to tell martial artists who's the strongest. Competitions are instead meant to be used as a measuring stick to show how far one has come and how much they still need to improve. If the Turtle School students won, they would grow arrogant and think they had no reason to improve themselves.
In order to push his students to improve, Master Roshi decided to beat them in the tournament. He wanted his students to know that there will always be stronger opponents out there, and that overcoming them will require further training than they currently have. Roshi had no way of knowing just how right he would be about this early on in Dragon Ball, but understanding that there's always somebody better is a good life lesson in general.
As for the alias, Roshi didn't want to be recognized by his students. If he went up against them as himself, there was a chance that they would subconsciously hold themselves back against their own master. He went into the Tournament as Jackie Chun so that they would fight him with everything they had when they lost. To this end, he removed his glasses, changed his clothes and glued a toupee to his head so that he'd be harder to recognize.
The Jackie Chun ploy turned out to be relatively successful. In the 21st World Martial Arts Tournament, Jackie Chun was pitted against Yamcha, Krillin and Goku and beat all three of them. Yamcha wasn't even his student yet. Regardless, Master Roshi was able to accomplish his goal and convince these boys to continue training, drawing out their untapped potential.
In the 22nd World Martial Arts Tournament, things went a little differently. Master Roshi competed again as Jackie Chun, but he was pitted against Tien Shinhan before fighting any of his students. It was a fairly even match, but Jackie Chun ultimately forfeited, leaving Tien to fight either Goku or Krillin in the finals. Roshi later explained to Tien that he saw him as a better opponent for his students and entrusted their future to him. With that, he retired the Jackie Chun toupee for good.
While Jackie Chun is gone, his spirit lives on in Dragon Ball Super. Here, Beerus convinces Goku and Vegeta that there's another fighter in their universe stronger than either of them-- Monaka. Of course, Monaka is actually a weak crybaby, but the principal behind him is the same as Jackie Chun. As long as Goku and his friends believe that there's somebody better than them, they'll be motivated to grow stronger and refine their craft.
