A shield grab is the act of grabbing while shielding. Generally it is used to punish attacks when they are blocked - in most cases the attacker will be caught in the lag of their attack, which means the defender's grab can often connect with little trouble. Using a shield grab allows a character to circumvent the slight delay that usually occurs after dropping the shield, so unless the character has a good out of shield option a shield grab is usually the best response.
Because grabbing input-wise is the same as shielding and attacking at the same time, shield grabs can be done simply by pressing the attack button while shielding, instead of pressing the grab button.
As a basic, simple technique, there are many ways around it, not in the least of which are cross-ups and/or shffls. However, it is still effective when used in the right situation; certain characters' grabs are so good, it is often worth the attempt, even if it fails. In competitive play, shield grabbing is most often used after shielding a high-lag attack.
If a player uses a shield grab after shielding an attack in SSB, the resulting throw will only deal half damage. It is believed this was to combat shield grabbing as the "obvious choice of action". This restriction was removed in later games.
 Video Demonstrations