Usually an O2 sensor. Located on the exaust pipe prior to the muffler.....looks like a spark plug with a wire that comes off the tip and leads into the wire loom.
When black smoke comes out from exhaust of car while driving the reason is that that the air fuel/ratio is too rich, and if the air/fuel ratio is too rich, more gas is being burned inside the engine combustion chambers. As you may not aware, one of the most common cause why the air/fuel ratio is too rich is a clogged air filter, when the air filter is clogged it will restrict the amount of air going inside the engine combustion chamber, with the less amount of air inside the chamber against the amount of fuel a black smoke is created during combustion. With that said, if you encountered a black smoke that comes out the exhaust of your car the first thing that is needed to be check is the air filter, check whether the filter is clogged or not.
When doing this just remove the air filter and visually check if there an accumulation of dirt on the filter. If dirt is present then it is more likely the cause of air/fuel ratio being rich. Fixing this one is easy you just have to replace the filter.
But for instance, there is no dirt present on the filter, then a possible cause of the problem has something to do with the car fuel injection system. Usually a problem on fuel injection system is the fuel injector sensor may be bad. The job of the sensors is to measure various engine factors that use to calculate how much fuel is injected into the engine cylinder, if the sensors gone badly the air/fuel ratio will be wrong which causes black smoke out the exhaust.
The sensor that is commonly cause black smoke from exhaust when at fault are the mass airflow sensor, throttle position sensor and engine coolant temperature sensor. It is difficult to identify which of the three sensors are the problem therefore the only thing to find this out is to bring the car to a reputable car shop and ask the mechanic to check the car with an engine analyzer, replace the sensor at fault to fix the problem. For car with carburetor the most common cause of black smoke problem is a stuck choke plate.
To find out if it is indeed a stuck choke plate problem, locate the carburetor and remove the air filter unit to be able to look down the carburetors barrel, examine the location of the choke plate inside the carburetor barrel, if the choke plate is nearly close or close then your car suffers from stuck choke plate problem and this is the cause why there is black smoke coming out the exhaust. To correct the problem apply choke spray to the choke linkage if this does not correct the problem you need a new choke. However after examining you found that the choke plate not stuck then the only remaining possible cause that makes your car to emit black smoke from exhaust is a vacuum leak, if this is the case then you'll need to bring your car to a reputable car shop and ask the mechanic to test your car for a vacuum leak.
Take this problem at once to avoid much bigger problem that may arise from having a black smoke from exhaust of car.
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