Boeotian (bee-ow-shan or bay-oh-shan) is a word with a literal and a figurative meaning. The literal meaning is anything relating to the ancient Greek region of Boeotia or its citizens. The figurative meaning is something dull; boorish or a person who is ignorant or lacking in culture.
This figurative view comes from the stererotypical views of Boeotia, which was just northwest of Attica, the region that contained Athens. Though Boeotia contained Thebes as well as smaller cities, and produced some well-known figures, it was never as united as the areas around Athens and Sparta were, and the struggle between the towns kept people from developing much that the other regions recognized as culture (despite such Boeotian figures as Hesiod, Pindar, and Plutarch). They also had a history of fighting their Athenian neighbors: they sided with the Persians during the Persian invasion, for which Athens invaded Boeotia and controlled most of it for 10 years, and later against Athens during the Peloponnesian War, so there was no reason for Athenians to regard Boeotians in a positive light. In Aristophanes' "The Acharnians" there is a long conversation between Dicaeopolis and a Boeotian that depicts the latter as pretty much a country bumpkin. Indeed, Brewer's Dictionary of Phrase and Fable says the name of the region comes from the Greek word for ox because there were so many cattle there (though it also gives a more myth-based story that Cadmus was led by an ox to the site where he was to found Thebes). Thus Boeotians were said to love agricultural and pastoral pursuits. The whole region was also supposed to have moist, thick air, so the Athenians used to say the people were dull and thick as their own atmosphere.
Since Athens produced the bulk of the material studied by medieval scholars, and the word "Boeotian" in English dates to the 15th century, the English word probably reflects the Athenian view of their neighbors. Sometimes the characterization was even expanded to the phrase "Boeotian ears, " meaning those unable to appreciate music or rhetoric.
Sources:
http://wordsmith.org/awad/archives/0403
http://www.hyperdictionary.com/dictionary/Boeotian
http://en.wikipedia.org/wiki/Boeotia
http://www.books.md/B/dic/boeotian.php
http://omega.cohums.ohio-state.edu/mailing_lists/CLA-L/2003/05/0123.php
http://www.brainydictionary.com/words/bo/boeotian137870.html
http://www.bootlegbooks.com/Reference/PhraseAndFable/data/155.html