Pokemon Sapphire Version

move tutors are only in fire red, leaf green, and emerald. move tutors were created because some moves that were once TMs in red/blue/yellow were no longer TMs in the later generations of the franchise.

so a move tutor is a person who teaches your pokemon a certain move only once just like a TM. if a TM were a person, they'd be a move tutor.

The moves listed under Move Tutor are, like bearzrnyce said, people who teach you moves only once. The move tutor in Fallabor town will let your Pokemon re-learn moves it forgot...

contining hyper_g's answer if it learned a certian tm and you want to teach it to the pokemon and you taught it you can relearn it.For exemple if you taught blaziken arial ace then you replace it with double kick,you can teach blaziken arial ace again.

the move tutor is in Fallabor town, he will let your POKEMON re-learn moves. but you need heart scales

He's in Fallarbor town, just left to the Pokemon Contest Hall. He'll reteach moves that your pokemon have learned before, and moves they could have learned during a level up, but didn't. He will do this if you give him Heart Scales.
If you're looking for the Move Deleter, however, he's in Lilycove to the right of the Lilycove Department Store. He will delete HM moves that otherwise can't be deleted.

Allright Dude. Go to Fallabar town and talk to the man. he will want a heart scale. Give it to him and choose a pokemon to learn forgotten moves. if this doesn't work, there is something wrong with the game!!!