From the Game's Introduction:
Monster Trainer is an RPG about hunting and training Monsters, for the purpose of competing against others and winning the title of Champion Trainer. An RPG, or role playing game, is a type of game where the players take command of simulated characters in a shared imaginative environment. There are many different kinds of RPGs; there are so many different games, that some consider classifying them all under the same title to be somewhat of a stretch.
In the imaginative world of Monster Trainer, there are a wide variety of mystical beasts, both wild and tamed. Someone has to tame the beasts, of course, which is where the players come in: each player has their own Moster Trainer to control. Players travel around and attempt to capture and train Monsters. When their beasts are ready, the players can seek other Trainers to challenge; each time you defeat the beasts of another Trainer, you can a higher ranking as a Monster Trainer. The goal of the game is to be the first player to gain the rank of Champion Trainer.
Resolutions in the game are made by rolling dice. With a very few exceptions, all rolls are made with one or more six-sided dice (these are the cube-shaped ones that come with most board games). When rolling the six-sided dice, you will most often be making a Normal Challenge. In a Normal Conflict, you roll the appropriate number of dice (indicated by a number followed by a letter 'd' such as '6d' for six dice), and count how many rolled 4 or more. You will oftentimes compare this roll with another roll, with the roll with more successes (rolls of 4 or more) being the 'winner'. The other rolls will be Special Rolls, which will have special rules unique to them, and may require specialty sized dice; note that if you don't have the special dice, you can use a number of playing cards equal to their number just as easily.