Is there a RAW definition of "revering nature" for the Druid class or is it assumed to be an up to GM discretion type of thing?
The terminology appears under the "Ex-Druids" language in the Druid class section.
The implementation of that line is entirely up to your GM. Tho only other mention of that phrase that I can find in the Pathfinder rules is in a 3rd-party Shaman class, which has the same restrictions that druids do.
This works similarly to the paladin's code. While the paladin's code specifically calls out a few examples of things that will break the oath, in the end it's up to the GM if a particular action breaks the code.
As a druid in my games, you probably want to steer clear of killing animals for no reason, clear-cutting forests, and spreading disease on the Savannah. However, you'll have to ask your GM for specifics.
It’s effectively the same rule as for clerics, who must remain true to their faith.
There is no rule stating what it means to revere nature, in much the same way there is no global rule for what is required to be a devout member of a faith. These are setting details: what does a given faith require, what does the cosmological force of nature require? A specific setting might have an answer to that, but you couldn’t write one that would cover all settings that you might play Pathfinder in.
If you are playing an official, published setting, you might find information along those lines in the material about that setting, but even there I expect it will be quite vague. These sorts of things are usually a matter of group expectations, which in many groups is largely dictated by the DM.