Why can a person with AIDS die from a simple infection?

AIDS is a syndrome that develops due to an individual's infection with human immunodeficiency virus (HIV).  This virus essentially inactivates the adaptive immune system of an individual of which it infects.  

The adaptive immune system consists of cell-mediated and antibody-mediated immunity.  Both branches require activation by helper T cells before they can actively combat pathogens that have infected the body.  Helper T cells, once they have been exposed to the antigens (cell surface markers)...

AIDS is a syndrome that develops due to an individual's infection with human immunodeficiency virus (HIV).  This virus essentially inactivates the adaptive immune system of an individual of which it infects.  

The adaptive immune system consists of cell-mediated and antibody-mediated immunity.  Both branches require activation by helper T cells before they can actively combat pathogens that have infected the body.  Helper T cells, once they have been exposed to the antigens (cell surface markers) of a suspected pathogen, will activate both cytotoxic T cells and also B cells.

Cytotoxic T cells can help to combat infections by producing and using toxic chemicals to kill pathogens and white blood cells that have already engulfed pathogens.  B cells, once activated, differentiate into plasma cells which can then produce antibodies that are specific to the antigens of the pathogen that incited the immune response.  These antibodies bind to the antigens of the pathogens as they flow through the circulatory system and, when bound, activate the compliment system which leads to the destruction of the pathogens.  Memory cells are also made in both branches so that the immune system can remember pathogens to which it has been exposed.  This increases the speed to which it can respond to the same pathogens in the future.

The problem with HIV and AIDS is that the virus specifically targets and disrupts the function of helper T cells.  If helper T cells are no longer functioning and no longer able to activate cell-mediated and antibody-mediated branches of the immune system, these systems are no longer available to fight infections.  Populations of pathogens may be allowed to grow uncontrolled except for controls due to the innate immune system (which may not be enough) and potentially lead to the death of the individual.