What is a manifold and a fuel injector and what do they do?
There are actually two manifolds on your engine, an intake and an exhaust manifold. Given the additional details you offered, I will assume you are speaking about the intake manifold.
Your intake manifold is a collection of pipes that carry the fuel and air mixture into each of the six cylinders on your Maxima. (Whereas the exhaust manifold is also a series of pipe that carry exhaust from each cylinder into the exhaust system.)
The fuel injection system is an electronically controlled apparatus for mixing fuel and air in the proper proportions for combustion and then spraying it into a fine mist to improve the quality of the burn in each cylinder when a spark is supplied by your spark plug.
This fuel/air mix then is distributed to each cylinder by the intake manifold.
That said, it is fairly uncommon for an intake manifold on a Maxima to fail. As most of them are metal and often even cast metal, the only failures come from being cracked or warped from a severe overheating. I would be rather suspicious of that being the case on your car.
Fuel injectors on the other hand often do get clogged up but can be cleaned with a fuel injection cleaner such as one of the BG products. When dirty they do not spray the fine mist necessary for good combustion and the car will run rough. Sometimes injectors also fail, but I would try a thorough cleaning before I drew that conclusion.
What is a manifold and a fuel injector and what do they do?
The intake manifold is what allows the air to flow into the cylinders, and the fuel injectors are what sprays fuel into the intake just above the intake valves. There is an exhaust manifold too, it routes the spent exhaust to the exhaust pipe from the cylinders.
