TITLE: Presheaves are locally sheaves?
QUESTION [7 upvotes]: On nlab it says that a presheaf is locally isomorphic to a sheaf. What do they mean by locally isomorphic? Their definition of locally isomorphic is given in terms of Grothendieck topologies which i think is overkill. 
When I first read the nlab page, I thought that it might mean that every presheaf, when restricted to a small enough open set is a sheaf, but I have doubts now because I can't find a proof in the literature and I can't prove it myself.

REPLY [4 votes]: Arrgh, I wish to delete this, but do not know how.  So i will make it into a question.  Georges' nice answer is a presheaf that violates the existence axiom s2 on every nbhd of a point.  Is there an example that violates the uniqueness axiom s1 on every nbhd of some point?