Answer:
The word merit is a term subject to various meanings, but in a legal context, merit refers to a claim which has a valid basis, setting forth sufficient facts from which the court could find a valid claim of deprivation of a legal right.
How this would relate to a 'trial' of the type the questioner asks about is unknown,
EXCEPT that what it might actually mean is that a judge is willing to hear a motion, an argument, or conduct a hearing, "based on its merits." This might mean that they will listen to an argument to detemine IF any valid legal grounds exist for them to consider. Such a hearing would probably NOT be conducted in front of a jury. Since the question was posted under "Divorce and Marriage Law" category, it is safe to say that such civil actions are NOT jury demandable.