Heart Containers are usually found after defeating a boss in a Zelda game. They increase Link's life bar by one heart.
A Heart Container can be formed by collecting 4 (or 5 in Twilight Princess) pieces of heart. Pieces of heart are spread throughout the games and can either be found in treasure chests or be given to Link in return for a favor.
In the Super Smash Bros. series, Heart Containers are one of the recurring usable items that appear on the battlefield. They heal 100% of the damage taken by the user (which may not be all, as the games allow for more than 100% damage).