On Wikipedia (http://en.wikipedia.org/wiki/%C3%89tale_fundamental_group) it's been written
In algebraic topology, the fundamental group π1(X,x) of a pointed topological space (X,x) is defined as the group of homotopy classes of loops based at x. This definition works well for spaces such as real and complex manifolds, but gives undesirable results for an algebraic variety with the Zariski topology.
I don't understand what "undesirable results" means, could anyone give an example?
It just means that the Zariski topology is too different from the topology of the interval for there to exist sufficiently many paths or homotopies between them. For instance consider $X=\mathbf A^1_\mathbb{C}$. Topologically, it is just the cofinite topology on the underlying set of $\mathbb C$ (with a generic point thrown in). Can you come up with a single interesting map from the interval $[0,1]$ to this space?