The basic idea is that trainers tend to do better for their main clients. They want to keep them happy! Also, when a trainer is running a horse for a new client they certainly want to make a positive first impression.
There is also information in this tab for the HORSE: number of lifetime starts, wins and days since last win.
When you click the OT tab you will see a table like this:
DAYS SINCE LAST WIN: The number of days since the horse last won a race. If a horse hasn't won a race in several hundred days, why do you think it will win today?
O/T MATCHES: The number of times the trainer and owner have run a horse (this is not limited to this horse, but includes all horses ever trained for this owner). People tend to focus more on their best clients...
O/T PLACE %: The percentage of time the trainer and owner place when running a horse.
O/T SHOW %: The percentage of time the trainer and owner show when running a horse.
There are many ways to interpret these stats, but as a general rule of thumb, looking at horses that have a large number in the O/T Matches column with a show % of higher than 35 is a good place to start (trainers want to keep their big clients happy by putting horses in the best spots to win). Also - pay attention to trainers that have never trained for an owner before (0 in O/T Matches) everyone want to make a good first impression.