There is an entirely unproven, but still popular, theory about who/what the Merovingian is. (Some of it is based on content from the various video games, especially the online one, but I'll stick to just the movies for now.)
We know that one of the key aspects of the last two Matrixes (the one from the movie and the subsequent "rebooted" one) is that choice was explicitly programmed in. That was the only way to prevent the majority of humans from rejecting it, but necessitated the whole cycle of The One, etc. We also know that previous failed versions of the Matrix did not have such free will programmed into them. One was a paradise version and one a nightmare version where the machines had complete control over every aspect of the bluepills' lives.
The speculation is that the Merovingian was involved somehow in the construction of one of those early Matrices, specifically, the second. The only canon basis for this is:
His very long speech about choice being an illusion, that cause and effect determined everything that happened. This is almost exactly how the second Matrix was built - the Architect put basic cause/effect programming to make the world "seem" to behave more realistically to the connected humans.
The fact that he has programs like The Twins working for him, who are later explained as versions of Agents from the second matrix. In fact, we see other "monsters" (like the "werewolf" Persephone kills with a silver bullet) -- the second Matrix was populated with all manner of monsters from human lore.
The general idea is that the Merovingian is a holdover program from that second matrix, either responsible for its design, or more likely part of its operation system. (I've seen claims that this last bit was "confirmed" but cannot find any official confirmation of it.) The reason he is dangerous is because he does not hold to the belief that choice is even a real thing, thus he is a danger to both humans and the Matrix as a whole. He represents a danger to Neo specifically because he doesn't agree with the Architect's vision of the Matrix and the path of the One, which (supposedly) explains why he tries to keep Neo away from the Source. It also explains his extreme hatred for The Oracle, who is the agent of choice and free will in the Matrix and thus his polar opposite.
Besides that, he likes to collect literal monsters.
BTW: The theory that he is a former One is a misunderstanding of a line from Persepohone, where she tells Neo that the Merovingian "used to be like you"; its clear from plenty of other dialog that he is and always was a program, but that he had met all of the previous Ones, and thus was not one of them. She's speaking more abstractly, about his attitude (probably towards Trinity).