Fresh air, or combustion air, intake is very important for proper functioning and safety of combustion appliances.
Stoves, fireplaces and, most importantly, furnaces use air when operating. Basically, the burned air that goes up the chimney has to come from somewhere. Think of it as if your home is a box with two openings, one the chimney and one the fresh air intake. The fresh air intake can be a window, or any other opening. It should be a dedicated opening that is unobstructed. There are several issues that a home inspector needs to communicate to their clients:
1) Plugged Intakes: I have seen fresh air intakes plugged with tape because homeowners noticed cold air coming into the basement or crawlspace from a pipe with apparently no use.
2) Improper Renovation: A great example of this, when a home was new, the furnace was in a large unfinished space in the basement. Then, perhaps years later, the home owner renovated and built a small furnace room around the furnace and water tank, with no consideration for the combustion air.
3) Change in Lifestyle: The previous occupant of the dwelling may have always had an open window, and the new owner may like to close the windows. For years it was relatively safe, and then new lifestyle leads to a dangerous situation. The issue arises when a bathroom fan, or a kitchen hood, is activated, the strong fan removes air from the home, and since the home is sealed tight, the dangerous exhaust gases are drawn down the chimney and back into the home.
4) Need for Proper CO Monitoring: When there is not enough fresh air, the gases going up the chimney are slowed down due to improper draw. Carbon monoxide is deadly and each home needs a functioning detector.
These are just some of the issues why the air may be compromised, and there are also many problems that result from inadequate air. A good home inspector looks for clues, they may be rusting or scorch marks at bottom of vent, or melting of plastic components.