When natural gas is burned completely, the resulting products are carbon dioxide (the same chemical that causes bubbles in a soda) and water vapor. Both products are usually harmless. Like most other fuels, the potential for carbon monoxide occurs when natural gas is burned incompletely.
Incomplete combustion can result in carbon monoxide which can be dangerous. That's why it is important to have natural gas appliances routinely inspected and serviced to ensure proper operation, including a check of vents and flues.
Another factor that may affect the safe operation of vents and flues is the availability of make-up air. Think of your home as a box. Just like humans, appliances need fresh air. You can't expect flue products to go "up and out the chimney" if you don't allow air in. This principle applies to any vented device (e.g., fireplaces and exhaust fans). The flue products themselves are not a problem as long as they are replaced by fresh air.
Without adequate ventilation, complete combustion will not occur. Instead of carbon dioxide being produced, carbon monoxide will be generated-a potentially deadly situation.