The Carroll Doctrine came out of a case : Carroll v. U.S., 1924 (267 U.S. 132). A prohibition era case, Carroll is the case which creates the constitutional difference between searches of dwellings and vehicles. After a review of a number of statutes, basically doing an original intent analysis, it states that for buildings a warrant may be easily obtained while for vehicles “it is not practicable to secure a warrant, because the vehicle can be quickly moved out of the locality or jurisdiction in which a warrant must be sought.” Going further it explains that an officer can't just stop any vehicle he wants to.
The measure of legality of such a seizure is, therefore, that the seizing officer shall have reasonable or probable cause for believing that the automobile which he stops has contraband  therein which is being illegally transported.To sum it up, Carroll allows LEO's with probable cause to search an entire vehicle because of the mobility of the vehicle and the difficulty of obtaining a warrant in a timely manner.
I can already hear the howls of protest. “In the modern world we have radios and cell phones. Carroll is outdated law!” Well, maybe so in your locality, but let's consider those of us in far Southwest Virginia. My county borders Kentucky. There are mountains everywhere, cell towers are extremely spotty, and there are plenty of places back in the way back, with three or four mountains between the deputy and civilization, where anything short of satellite communication just ain't going to work.
Consider a case wherein the local sheriff's department has all sorts of knowledge of John Jones trading oxycodone, methadone, suboxone and lortabs back and forth across the Kentucky-Virginia border in his SUV. Jones crosses the border at random times and places. At 3 a.m., Deputy Smith is out in the way-back returning from a call from a house just on the other side of a national park. He sees Jones driving an SUV down a road which comes directly through the park from Kentucky (with no civilization anywhere near either side of the border). Pulling over the vehicle, the deputy sees nothing in plain sight and Jones is savvy enough that he's never going to agree to a consent search. There's no cell service anywhere near and the mountain next to the road isn't letting any radio waves get through.
Deputy Smith is faced with a number of bad choices. If the deputy releases Jones, so he can go get a warrant, Jones will be back across the border in 5 minutes. If the deputy secures Jones in the back of his car while he drives 10 miles down the road where he can get radio contact he has extended a seizure of a person without an arrest. The least constitutionally intrusive practical act is a search of the vehicle on the scene.
In the modern era, the use of Carroll assumes that smugglers are smart enough to try to ply their trade in areas where it will be difficult for LEO's to easily get search warrants. If a smuggler is stopped at a port in Miami or driving through New York City local LEO's probably shouldn't be able to rely on Carroll. On the other hand, in a rural county in Nebraska where there are two deputies on duty and the judge comes by once a week, Carroll may be a necessity if there is to be a realistic possibility of actually enforcing the law.
[addendum] Apprently, my reading of Carroll was too restrictive. Via Commonwealth v. Grimes, I see that the federal supreme court has entirely excised any exigent circumstances requirement so that all an officer needs to do the search is mobility of the car and probable cause that contraband is in it.