Why does 三八 mean gossip?
I believe it is understood throughout China, but it may sound 'Southern' to Northerners and it wouldn't be their word of choice when they want to express the same meaning.

There are two possible origins:

According to Baidu Baike, 三八 means 三八妇女节 (International Women's Day on March 8th), which is extended to refer to women in a derogatory sense, most commonly used against women who appear crazy or maliciously gossiping or interfering with other's business.

Wikipedia says it's because when China first opened trade with foreigners, the foreigners were permitted into the city on 8th, 18th and 28th of every month, locals call seeing the foreigners 三八 (the three eight's), extending to anyone who's overly interested in fresh things, peeking secrets or gossiping.

I am from Beijing. People around me all share the first explanation, but maybe people from the south find the seconds one more sensible.