I have a multiple-entry Schengen visa valid for three months. Recently I traveled to Germany, Paris and Italy, then back to my hometown. Since I have a 3-month visa, can I travel again to another country in the Schengen area?
Entries go for the Schengen Area, not the countries within, so for your trip to Germany, Paris and Italy you only had one entry.
As no one (in Schengen) cares whether you go home or somewhere else that you're allowed to be, multiple trips (to Schengen, whether you consider them multple trips doesn't concern the Schengen countries) is pretty much the only thing you can use a multiple entry visa for (within the other rules - validity period and 90/180 - of course).
Multiple entry implies that you can enter and exit the area multiple times, as long as your visa is valid (provided border guards let you in).