Last week, the government of Pakistan decided that YouTube was anti-Islamic and told the local ISPs to turn it off. This they did by announcing to their local Internet that they now owned the address block where YouTube lived. Thus, any requests to YouTube's California servers found themselves routed to Pakistan - where YouTube wasn't.
So far, so bad. But then, the change found its way to Pakistan's upstream provider - PCCW in Hong Kong - which accepted the new announcement and propagated it outward to the rest of the world. As the change rippled around the planet, YouTube effectively vanished. Some hours later, the problem had been diagnosed and things started to get back to normal - but not before some people had reported no connectivity for more than a day.
As with most incidents with unexpected consequences, there appears to have been a chain of mishaps. It is most charitable to assume that Pakistan didn't mean to hijack YouTube globally and either didn't know what the effect would be or pressed the wrong buttons. Similarly, it's best to say that PCCW mistakenly passed the announcement on, when it would normally verify it first, rather than being set up to relay all such things automatically.
This does highlight the sensitivity of the Internet's routing mechanism - such route poisoning isn't unknown or particularly rare, but that such a high profile provider got hit so badly by mistake is a very bad sign for what might happen if malicious intent is injected.