In this post-apocalyptic world, probably brought on by nuclear war, pretty much everyone has been exposed to lots of radiation and it seems many of the War Boys have cancer.
Nux is having night sweats and enlarged lymph nodes in his neck, so I'm guessing he has some lymphoma, a type of cancer that involves lymph nodes.
In patients with cancers of white blood cells (leukemias and lymphomas), the bone marrow is overcrowded by defective, cancerous white blood cells, so the bone marrow has neither the resources or space to make red blood cells, which are necessary to transport oxygen.
As a result, when the cancer gets bad enough (such as when you don't get treatment), blood transfusions will often be necessary.
This way the blood recipient can get the donor's red blood cells to prevent anemia and platelets to prevent bleeding.
This is not a cure for the cancer, but it should help with some of the symptoms.
Max probably has blood type of O-, making him a universal donor, so people use him as a "blood bag."
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Its alluded to in the opening monologue that pretty much everyone has some form of cancerous disease.
Hence transfusions, Larry and Barry the tumours, etc.
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I presumed that many of the War Boys have a lymphoma due to radiation or inherited mutations.
It was details like this that elevate the movie.
Furthermore the "oil" barron who had terrible lymphedema with his bulging feet made the movie all the more "realistic" and disturbing.
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Nuclear bombs, radioactive warfare, they are all referenced to as "half lives" - they are or were obviously exposed to radiation.
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The War Boys are all sick one way or another and have shortened lifespans, so they need blood transfusions to live longer and hopefully live long enough to become drivers.
They probably have lymphedema, anemia, maybe leukemia, since that is also treated by blood transfusion.
It might also be to get adrenaline, since Nux brought Max, his "blood bag", with him on the ride.
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In the new  Mad Max: Fury Road , a major starting event is that Max is being used as   a "blood bag" for one of the War Boys.    It seems to be implied later on that    the war boy has some sort of terminal illness (indicated by the two strange lumps on his collar bone and a mention of night fevers).    Is it ever actually explained  why  they're receiving blood transfusions and/or what precisely is going on with the War Boys?
What’s going on with the War Boys in Mad Max: Fury Road?
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Nux has night sweats and enlarged lymph nodes in his neck, so he may have some lymphoma, a type of cancer that involves lymph nodes, treated by blood transfusion. This may be due to exposure to radiation in the post-apocalyptic world. The War Boys are all sick due to the effects of radiation exposure and are likely all suffering from some form of cancer that is being treated by blood transfusion. 
In this post-apocalyptic world, the War Boys are all sick and are most likely suffering from some form of cancer due to radiation exposure for which they are receiving a blood transfusion. 