Autoplacing is where the program places the parts automatically, according to schematic.
Autorouting is where it draws all the traces automatically.
Autorouting is very useful, Eagle does it. Autoplacing, generally not so much. Eagle does not do it, though Protel does. The designer often has a better idea of where things should go though. Autoplacing usually results in undesirable layouts, they may be confusing to inspect and important traces (high power, noise-sensitive signal) may end up getting run a long way between components. For example, say you have 4 buttons with identical pullup resistors, you'd generally want them to be in a nice parallel row but it's unlikely Autoplace will do this. They'd get scattered in different orientations and locations.