Expert is usually given soon after a member reaches 6,000 points on Pokebase. They don't really gain any privileges because being able to edit is given automatically at 6,000 anyway.
The only difference is that they can edit posts on RMT or Meta even if they are below the threshold for that (currently 1,000 and 2,000 respectively).
P.S. I removed the BA from the other answer, because it's not really correct. Sorry, Exca.
It would be nice if people waited for more answers instead of giving BA to the first post that comes along.