A hero with sustain can effectively keep their health or mana high through passive or active abilities in order to stay in lane forever. A good example is life steal, where one can hit enemy minions with basic attacks (an infinite resource) in order to heal oneself.
A bad example would be someone who heals upon being hit by an enemy, since they will always take more damage than they heal, and thus they cannot use it to sustain themselves in lane forever.
Heroes with sustain are generally much stronger laners than those without.
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