The first death is particular judgement. Your body remains on Earth, but your soul goes to either Heaven or Hell.
Theologians struggled with this for a while. They even brought up notions of Limbo and 'in between' circles of reality, which is not an altogether dead subject among them today even still.
But the general consensus in Catholicism is that your soul is either banished to the depths or ascends into a preserved state of salvation. When the time comes for final judgement, your soul is returned to the body, and both go their final destination.