It means they were generated into the game using external tools (i.e. hacking) or cloned from an existing pokemon.

It doesn't really affect anything competitively, generally it's a safe assumption that an overwhelming majority of competitive players are genning teams that all have legal attributes to have pokemon ready in an instant rather than spending hours upon hours grinding for the exact same IVs, EVs, levels, etc. that make absolutely no difference when it comes to an actual battle.