The reason we breathe is to get chemicals like oxygen into our lungs. But we also breathe to get chemicals like carbon dioxide out of our bodies.
The lining of our nose and throat contain mucus and cilliary cells that trap and remove particles of dust in the air we breathe. These get several chances to remove particles, since the air moves past them as we breathe in and out, and the dust particles have a good chance of being collected before they actually touch the surface of the lung.
When smokers inhale cigarette smoke, it is to get the chemical nicotine into their lungs, where it then enters the bloodstream and is carried to the brain. Other molecules from smoke also enter the blood this way, such as carbon monoxide. It holds on to the hemoglobin in the blood more strongly than oxygen does, so less oxygen gets to the brain and muscles.
Other molecules in smoke get into the bloodstream or lodge in the lungs, where they can cause lung cancer, or cancer of the mouth, throat and larynx.
Some chemicals around the house are very irritating to breathe. Ammonia and bleach both contain strong alkalis that can damage the cells they contact. Some metal polishes contain acids that also damage cells.
Some chemicals can make you dizzy or cause unconsciousness. Doctors and dentists have you breathe molecules like nitrous oxide (laughing gas) or chloroform to make you sleep through what would otherwise be a painfully unpleasant experience.