Last I checked, there's several factors - with credits being far and away the most predictable and effective - to ranking exploration.
Credits earned in explorer rank is the main driver:
- Passenger Tour-the-Galaxy
- Passenger Research (Deep Space)
- Planetary Scan Missions
- Turning in Exploration Data (the most common)
Beyond credits, you also have SRV distance driven - it's very minute. Though it
does scale with distance from Sol. In other words, a kilometer driven at Beagle Point is worth more experience (dunno how much) than a kilometer driven in Sol.
To my knowledge, filling out the Codex, unique to you discoveries, and such don't grant any experience - beyond the credits you might earn from those actions.