I keep seeing stables have remarks that their horse is strong in something and weak in others. How can I figure out that for my horses?

This is determined primarily by looking at what bars the horse has gained or not gained during training. Depending on the horse's rating, gender (geldings and CS mares train faster) and what it's training in (single discipline versus all disciplines/eventing), you can compare it to the "ideal" training for your particular situation and determine whether it's strong or weak in a certain discipline or singular training area.