Roughly speaking, for a variety or scheme X, the idea is to consider étale coverings U \rightarrow X and to replace each connected component of U and the higher "intersections", i.e., fiber products, U_n := U \times_X U \times_X \dots \times_X U (n+1 copies of U, n \geq 0) by a single point. This gives a simplicial set which captures some information related to X and the étale topology of it.
