The limbic system is not the cognitive center really, unlike another answer suggests. That role is absolutely more accurately given to the prefrontal cortex, whose large size in homo sapiens is what gives us the power to process logic at high levels, and thus differentiate ourselves from primarily instinct-driven "animals". What the limbic system is primarily involved with, is emotional processing, motivation, behavior, but primarily — emotion and the general "emotional coloring" our individual perceptions have (if this doesn't make sense, please ask me to clarify).
So he is saying, by being a limbic system on legs, that he sees his (current) existence defined by his emotional overwhelmed-ness. He is not a creature of logic, for the present, but rather a creature defined by the deluge of emotion he is currently experiencing. As for the waterfalls — the physical expression of nervousness or whatever — just provides a corporeal example of his emotional state, while the limbic system mention refers to the more ethereal/intangible element of his emotional state.