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User recovers 1/16 max HP, rounded down, at the end of each turn.
Leftovers is generally used to restore lost HP, and often allows for extended longevity. Leftovers may often be used on offensive Pokemon so that passive damage does not add up so quickly, allowing a sense of bulk on sweepers over Pokemon with items such as Life Orb. Leftovers are often used on defensive Pokemon as a way of gaining back HP with ease.
Offensively, the extra turns bought through a stable item in Leftovers can often allow Pokemon to have more than one turn setting up, thus allowing for a higher chance of a sweep. For example, if a Dragonite with Life Orb could only manage one Dragon Dance, the overall boost would be x1.95, but if a Dragonite with Leftovers managed to get two Dragon Dances courtesy of the additional HP, the overall boost would be x2, on top of the 6.25% health gained per turn. As previously mentioned, defensive Pokemon often use Leftovers to save EVs against certain offensive threats, as the extra HP gain may allow for less EVs to be used defensively, allowing the additional leftover EVs to be placed elsewhere.
While Leftovers provides HP, there are also some downsides. The extra HP will often be useless on a sweeper, and therefore the power lost through item choice can be devastating for a team, as it may leave certain Pokemon unable to KO the opponents when specifically needed. While EVs can be saved, the EVs not used defensively due to the effect of Leftovers may leave a Pokemon in danger to threats if sandstorm or hail is in play.
When using Leftovers, it is often advised to make your HP divisible by 16, +1. This will allow for a "magic" Leftovers number (a number divisible by 16), while the +1 allows essentially for a "free" hit point due to the floor function in the damage formula.