In the latest news you can find out more details about exploration but more will be covered later. And as they say you can make money by this activity. And going through systems is not a valid explored system. You will have to scan it, go to the vicinity of scanned planets, moons, anomalies etc. Scanning will be active and passive so you need to use both to check planet types, chemical composition, mineral deposits and so on.
Active scanning is needed for greater details of selected planet. But you should be careful all the time because other players or npc can appear and kill you.
But how will you get payed by this activity? Information about new systems, planets and other logged data will earn you money by selling it to a data claim registration facility.