I remember it as being a more substantive (in terms of number of matches) rivlary than it actually was. Courier led 6-4. Their primes didn't really overlap, maybe briefly. Not surprisingly, most of Edberg's wins were earlier in the rivalry. Most of the ten matches had the losing player taking at least a set.
They played in Slams six times I think. Edberg beat Courier in 5 sets at the 1990 French Open, only to have Courier return the favor and beat Edberg in 4 sets at the 1991 French Open. I'm sure no one was expecting Edberg to then, later that year, absolutely destroy Courier in the 1991 USO final, in what was probably one of Edberg's greatest matches. From there, Courier had a bunch of routine 4-set wins (that were never really in doubt) against Edberg in Slams, incuding the 92 and 93 AO finals, and the 93 Wimbledon semis. Courier beat Edberg in Scottsdale in 3 tight sets in 1995, when Courier himself had started to go downhill a little. [Note: I haven't accounted for all 10 matches].
It was a good matchup, contrasting styles. Courier "having Edberg's number" wasn't really anything specific. I don't think he was in Edberg's head. 92 and 93 were arguably Courier's prime and Eberg had dropped off just slightly, which was enough to result in those routine 4-set wins at Slams that I referenced.