Roughly speaking, for a variety or scheme X, the idea is to consider étale coverings
and to replace each connected component of U and the higher "intersections", i.e., fiber products,
This gives a simplicial set which captures some information related to X and the étale topology of it.
Slightly more precisely, it is in general necessary to work with étale hypercovers
Taking finer and finer hypercoverings (which is technically accomplished by working with the pro-object in simplicial sets determined by taking all hypercoverings), the resulting object is the étale homotopy type of X.