"... the gap between performance and the potential level, and shows that in the gap -in the zone of proximal development - children are assisted to move beyond what they have shown they can do in everyday activities by having their learning scaffolded, using cultural tools,..."
This is from Introducing Vygotsky by Sandra Smidt (2009) which is actually written for early childhood educators. ZPD is defined as the gap between performance and potential. It is in this zone that children are helped to move beyond what they can do with scaffolding.
That means at the performance level, children can do some things on their on but they are not able to do, say, X. In the zone of proximal development, they are able to do X with help. The potential is that the children can do X on their own.
Let's look at a few other explanations of ZPD.
The zone of proximal development, often abbreviated ZPD, is the difference between what a learner can do without help and what he or she can do with help.
Vygotsky stated that a child follows an adult's example and gradually develops the ability to do certain tasks without help or assistance. Vygotsky's often-quoted definition of zone of proximal development presents it as "the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance, or in collaboration with more capable peers."
Vygotsky among other educational professionals believes the role of education to be to provide children with experiences which are in their ZPD, thereby encouraging and advancing their individual learning
From H Coffrey (UNC School of Education) wrote
The zone of proximal development is the gap between what a learner has already mastered (the actual level of development) and what he or she can achieve when provided with educational support (potential development).
From L Vygotsky (translated by M Cole)
It is the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers. (p. 84)
Reference: Vygotsky, L. (1978). Interaction between Learning and Development (pp. 79-91). In Mind in Society. (Trans. M. Cole). Cambridge, MA: Harvard University Press.