Egg Lay is an attack in the Super Smash Bros. series that is based on the swallow move in the Yoshi series. So far, it's appeared in every game in the series, which includes Super Smash Bros., Super Smash Bros. Melee, and Super Smash Bros. Brawl for the Nintendo 64, GameCube, and Wii respectively. It's the standard special attack of Yoshi's.
When you press the B button, it will cause Yoshi to launch his large and sticky tongue out. If it touches an opponent of his, he'll engulf the enemy and thrust him into an egg. After a couple of seconds the trapped opponent will be able to free him or herself, contrary to that of the Yoshi series, where the enemy would be trapped forever.
In the three Super Smash Bros. video games, Kirby is capable of sucking in his opponents and copy their abilities. If he does so to Yoshi, then he'll gain his Egg Lay ability. This ability will disappear if he is attacked a certain amount of times, if he dies, or if the user controlling him taunts.