Turbo-annexing only works in versions 1.2 to 2.1, and not in any of the later expansions. In these versions, turbo annexing is the fastest way to annex a country with many provinces.
Beginning in EU3 v1.2, the AI became much more stubborn at accepting peace terms that cede many regions to the conquering nation. Thus, a new method had to be found for those impatient players who didn't want to slowly eat a large nation via multiple wars and multiyear truces.
The basic concept is to "break" a nation, having rebels take over their government and your country taking advantage. When rebels control more provinces than the current government controls, the nation breaks. All wars end in truces and the current leader is deposed for a new leader. But more importantly, all provinces except the capital are ceded to their occupiers. This is called turbo-annexing.
First, conquer every province the target country owns except one. Second, make the remaining province revolt. You could look for a country that happens to have a rebelling region and use that rebellion to your advantage. The other option is espionage. The crux of the spy work is the support revolt. It would also be useful to sow discontent until they are at -3 stability to make that easier, though since that is a hundred ducats a try, you would want to first use spy ring infiltration to increase your odds of success. After your spy missions, wait for a rebellion to arise, and then wait for the rebels to win the siege against the province's fort (if any). (You could use a spy to bribe defenders to speed this along.) Finally, the end of the month, all the provinces that you had occupied, except the capital (and not including the revolting province), are annexed to their occupier—you.
Effects and Strategy: Most importantly, this allows you to take almost all of a country's provinces at once. For those provinces on which you do have a core, you receive no BB points. You also enter into a 5 year truce with the country, per usual after a peace treaty. The downside is that each province on which you don't have a core comes at a +1 higher BB cost as compared to if that province were ceded as part of a Peace negotiation. You also don't get the benefit of making the capital your vassal or having the other options you would in a peace negotiation. Note that this method will be quick ("turbo") in the sense that it does not take many wars to conquer all but one or two of an enemy's provinces, but it may take several months to cause a rebellion that is required for this method. It also requires strong superiority over the target country and some intricate espionage or timing. The higher BB cost for doing this is actually a good thing for people who like to win the game via badboy wars, but it could destroy your country if not careful.
Variations: The best method is to target the country's capital with the required rebellion, as that maximizes the provinces you gain and leaves them with only one. But, it is harder to cause rebellion on a country's capital, as it is the most stable. The alternative and easier method is to conquer the capital but target a different province for rebellion. It will naturally be easier to stir up a rebellion because it is not the capital, and you can make it even easier if the province has a different culture and religion than their capital. This alternative will leave them country with two provinces (the capital and your target for rebellion) rather than just the capital.
Turbo-annex does not work in NA after 2.1, IN or HTTT. However, at least in IN, if you get an enemy up to 15 war exhaustion while having less than 5 war exhaustion yourself, their provinces of cultures other than their primary culture can slowly start to defect to you by event.