Peeling describes the act of reactively protecting an ally or carry, which can be achieved through a variety of possible actions.
Peel by damage
The simplest way to peel is by dealing damage to the enemy, either to make their attack disincentive, or to dispose of them. This also is the most ineffective way of peeling- most champions that have a way to close in on an enemy also possess means of avoiding, negating, or reducing damage. They can also build sufficient defensive values to survive their dive. Peeling by damage mainly works when ahead or when abusing critical mistakes made by the enemy.
Peel by stat change
Another fairly simple way to peel is by decreasing the enemies stats besides health, or increasing the allies' stats. This can occur by casting abilities and building items with utility.
Examples of defenses that change stats:
Exhaust lowers both the enemy's damage and 
movement speed.
Redemption heals allies and damages enemies.
Janna's Eye of the Storm grants an ally attack damage and a shield.
Peel by interception
Many 
divers and 
assassins possess gap-closing 
dashes that can allow them to get in and get out with a kill within a moment's notice. To prevent their quick high damage, it is critical to either halt their attack, or prevent them from engaging on their target in the first place. This can be achieved by using 
crowd control on the enemy that is closing in. While all hard CC will render the aggressor unable to act, only 
knockups will stop a dash that is already being executed.