Moved to the more correct section of the Forums
A Trainoff is a contest organised and held by a player.
It typically involved training one horse (typically given to participants by the organiser) in an event, and then eventing that horses against the other participants of the trainoff. The winners then win prizes.
That's the basic gist. Many many variations are possible. Suck as training more than one horse, and entering each of them in different disciplines. Sometimes the trainoff horses are allowed to enter normal events as well.
Each trainoff has it's own sets of rules