Gehinnom isnt simple.
generally you are correct
it is a terrible awesome process of cleansing.
there are those that burn for eternity (hitler, bilam for example, i think korach also). this is a pure punishment.
there are many opinions among the Meforshim as to what the punishment is, but most agree that no one alive really knows.
the name gehinnom comes from the valley (ge) of Hinom in Yerushalaim where they would burn certain tamei things. there was always a fire burning there.
some say gehinnom is an intense, almost intolerable shame over your aveirahs that are visible to everyone
some say it is Hashem laughing at ones foolishness.