The monster alphabet is a system of hieroglyphics that are almost universally understood by monsters. While most monsters are intelligent enough to learn to speak in human tongues, others stick to their own species language or dialect (for instance, Tigers have a series of barks, growls and roars while Mocchis have a cute squeaky sound to them).
The alphabet was created at some point (possibly under the reign of the Three Beast Gods) to aid communication between the species. You can tell in the anime series that different monsters have a different grasp on the human language (i.e., while Worm cannot speak it at all, Mocchi and Golem have a rudimentary knowledge and Tiger and Hare, the two with the most contact with humans, can speak it fluently).
The ancient Pendant people used the monster alphabet to encode monster DNA into slates, and the monster alphabet is now taught at most higher learning institutions such as Barba University and Torble University. It is mentioned in Monster Rancher Battle Card 2 that Tesca is a master of the language.