Interestingly, this quote was used in a recent episode of "Bones" with David Boreanaz. Lovers and Madmen rarely use the logical aspect of their brain. There is no reasoning. Their imagination and emotions allow them to see the impossible, the possible, and to create completely unique perspectives. Using this sort of approach to the world opens up avenues of thought that a logical thinker iwll not see. Logic follows a pattern and does not allow for creative thinking. Hence, the flexible, open mind will perceive more of the world than those guided by the narrow and confining path of logic.
Ah, a great line. This selection means that lovers are like crazy people. Both of them have "seething brains" (a lot of weirdness in their minds, so much so that it seems like they are bubbling). They use their fantasy to understand the world, and to reshape it, and as they do so, they understand more of the world than people who are completely rational.
(Think of a singer or poet compared to Data or Mr. Spock from the different Star Trek films.)
It is a shakesperian quote that refers to the passion and delusions individuals who are in love or those who are insane suffer from.
EXAMPLE: A man or woman in love can become insanely jelous over things only their obsession sees.
While a outside observer with no emotion involved would not and could not begin to understand the reasoning involved in such a emptional response.