So what do the stats actually do?

[Jewelz^]

Stolen from GTA Wiki

Player stats appear once again in GTA V and GTA Online. The stats include Stamina, Shooting, Strength, Stealth, Flying, Driving, Lung Capacity, and Special. These stats start out different for each protagonists, but can eventually be maxed out.

• Stamina. Extra stamina will allow the characters to sprint, cycle and swim for longer before getting tired. When the character's stamina gets depleted, the normally green health bar will start flashing red, causing gradual damage to the player if they continue the actions and drop down exhausted when the bar gets too low. The stat will increase if the player perform each of those activities. Maxing out Stamina will allow the character to perform these strenuous actions indefinitely with no fear of health loss.
  
• Shooting. A higher Shooting stat will make the character more accurate by reducing recoil while shooting any gun. The character will also be able to reload faster and carry more ammunition to a max of 9999 bullets per gun category. The more targets the player hits, particularly headshots, the more his Shooting stat will increase. Spend time in the Shooting Range at Ammunation and take on shooting challenges as a fast way to improve this skill.
  
• Strength. Additional strength will inflict heavier damage during hand-to-hand and melee combat, increase speed at climbing ladders, increase damage reduction from falls, car crashes, explosions, gunfire, physical attacks, and fire, and improve the character's Tennis and Golf performance by allowing him to hit the ball harder. Engaging in unarmed combat, and taking part in sports like Tennis, Golf and Yoga will raise the character's Strength.
  
• Stealth. The higher the Stealth stat is, the quieter the character will be in both stealth and normal movement modes, and he'll also be able to move more quickly in stealth mode. The Stealth stat will increase the more time you spend moving in stealth and especially performing silent takedowns. Press L3 to enter stealth mode and again to exit it.
  
• Flying. When a character has a low Flying stats, the performance of any aircraft he's flying will be more susceptible to the effects of turbulence. As the stats increase, the character will be able to both fly and land more smoothly, and also will improve the ability to fly any aircraft. Just spending time flying steadily will increase the stat, whereas the Pilot School will make the process a lot faster by completing its challenges.
  
• Driving. Improving the Driving skills will improve the character's vehicle handling when airborne and make performing wheelies easier. The more time the character spends driving vehicles, the faster the stat will increase, particularly performing wheelies and landing big jumps on four or two wheels.
  
• Lung Capacity. Having a high Lung Capacity means the character can stay submerged under water for longer and the Oxygen Meter will decrease more slowly. Lung capacity will increase as the character spends more time under water, whether with or without the Scuba Suit.
  
• Special. Using a character's Special Ability will gradually improve the stat. As the stat bar increases, the speed at which that character's Special Ability bar fills up will also increase, and as it's active, the bar will deplete more slowly, allowing more time to use it. Only available to Franklin, Michael and Trevor, as the Online Protagonist doesn't possess any Special Ability.
  
• Max Health. Exclusive to the Online Protagonist, Max Health will Increase by 1 point every level up to level 100. Every 20 levels, the Max Health stat bar will show up with the corresponding number (20 for level 20, 40 for level 40 etc.). When the player has Max Health - they can survive a Heavy Sniper shot to the Stomach or Lower Torso with minimal health.
  

[BrotherTobious]

Oh look the driving stat does help you driving.... who would of thought jewelz

[Galatoni]

Really handy. Nice

[Jewelz^]

Oh look the driving stat does help you driving.... who would of thought jewelz

Technically, it helps you fly