Passive shield
In addition to the bubble shield common to all characters, Link, Young Link, and Toon Link carry their own personal shield while in battle.
While standing still, incoming projectiles that hit the shield will deal no damage and simply push Link back, dependent on how much damage and knockback it would ordinarily do. Unlike other projectile-countering abilities (like reflectors or the default bubble shield), this shield cannot break and can block any amount of projectiles regardless of power. The only exceptions to this rule are Young Link's Deku Shield in Melee (as powerful projectiles will pierce through it), and Link's shield in the original Super Smash Bros., which is only aesthetic and has no effect on gameplay.
Link's shield effect was first implemented in Super Smash Bros. Melee and has been retained in all installments of the series since then. Link's shield in Super Smash Bros. 4 was altered slightly - Link now takes a defensive stance when hit, and his shield is also active while he is walking.
Since projectiles must hit the front of the shield to be blocked, Link may still be hit in the back, head, or feet, and some idle poses can cause Link to move the shield away from the front of his body. Smash 4 altered his poses so it will not be disabled. Crouching will cover Link's legs and disable the idle poses, but then any projectiles that would have hit the shield normally may instead hit Link's face. Link's shield is unusable when he is holding an item.
To be considered a projectile for the purposes of the shield, a hitbox must be reflectable and not unblockable. It does not actually matter whether the hitbox is attached to a projectile; Falco's Reflector in SSB4 is blocked by the shield, even though its hitbox is attached to Falco himself.
Origin
Link has always possessed a shield in every The Legend of Zelda game to defend himself against attacks. Depending on the game, it may be an always-active ability so long as Link is standing or walking, or it may have to be raised manually; in either case Link must be facing the attack in order to block it. In some cases, powerful attacks are too much for the shield and may cause Link to stagger or damage him anyway.
The design of each Link's shield is taken from their respective game. In all games, Link carries the Hylian Shield, which debuted in The Legend of Zelda: Ocarina of Time and retains a similar design across incarnations. Young Link uses the Deku Shield from Ocarina of Time (which does not burn against fire, unlike its original counterpart), while Toon Link holds the Hero's Shield from The Legend of Zelda: The Wind Waker.
Link being capable of shifting his shield's position by crouching is reminiscent of Zelda II: The Adventure of Link, where Link can either defend his upper body or lower body by crouching and standing. In addition, one-handed swords in The Legend of Zelda: Ocarina of Time and The Legend of Zelda: Majora's Mask would cause Link to crouch if he shielded without Z-targeting.
Gallery
Link blocking an arrow in Melee.
Young Link blocking a projectile in Melee.
Link blocking a projectile in Brawl.
Toon Link blocking a projectile in Brawl.
Toon Link blocking a projectile in Super Smash Bros. for Nintendo 3DS.
