For structural isomers, "different arrangements in space" means the connectivity of the atoms are different. For example n-butane and 2-methylpropane are structural isomers since they have the same molecular formula but the atoms are bonded together differently.
Structural isomers do not include different rotational conformations of molecules or molecules that are "mirror images" of one another since the connectivity is not different. These are classified under different types of isomers (rotational isomers and stereoisomers respectively). For the rotational isomer case, use a model kit to build n-butane. You will notice that you can twist the atoms around the bonds as much as you want but the atoms will have the same connectivity, so the different rotational conformers will not count as structural isomers.
Hope this helps some.