It can be both actually.
If software, its basically plug-ins that you apply and shape your vocal track after recording it.
If you prefer to have realtime outboard effects or hardware I can honestly say you will have to fork out some big bucks to get a descent one.
I have tried several over the years only to take them back because they simply sucked. The cheaper ones are more less special effects in my opinion. I could get the same effects running a mic thru a guitar processor.