From several lecture notes and some posts, people claim that while scheme is constructed by gluing affine schemes over Zariski topology, algebraic space is constructed by gluing affine schemes over etale topology, which I do not really understand. Could some one explain this point carefully? Examples?

From several lecture notes and some posts, people claim that while schemes are constructed by gluing affine schemes over the Zariski topology, algebraic spaces are constructed by gluing affine schemes over the étale topology, which I do not really understand. Could someone explain this point carefully? Examples?