It means to talk about things in great detail, listing every facet of their being. Also to have the ability to speak at great lengths about nothing.
I speak a very verbose english language
Verbosity is the ability, limited in the general population, to utilize words which may be archaic, lengthy, and in the English language are more often than not based in Latin. Quite often, the phrases used in such a manner are synonymous with much more succinct forms. In addition to the expansive vocabulary utilized, prose which is deemed 'verbose' will quite often feature parenthetical phrases in unusual frequency, as might be found in scientific journals or university textbooks. Though accepted in academic contexts for its ability to explain, in great detail, concepts which may seem rather complex to the average layperson, the overuse of excessive verbosity will often cause common folk, especially those who might be afflicted with the neurological disorder known as Attention Deficit Disorder ( ADD), to lose interest in the concepts being explained, and thus the knowledge they might gain would be lost to them. Moderation, therefore, is the key to the proper usage of verbosity.
It's good for padding English essays, and there's a type of thread on 4chanthat shows up every once in a while where people talk like that for the lulz.
Person 1: Should you deign to learn the definition of Verbose, one needs only glance upwards, and focus one's eyes on the paragraph above.
Person 2: Uh, you lost me at "deign."
See logorrhea, excessive, long