When you have bad breath, the odor that comes from your mouth and nose is not just the smell of undigested food or dead cells. It is not only the smell of mucus or post-nasal drip, either. Much of the odor of halitosis comes from volatile gases produced by microbes in your mouth.
As you smell a person's breath, oftentimes much of what you're detecting is not the smell of food or beverages lingering on the tongue. Instead, you are noticing molecules given off by the bacteria that are feeding on those particles.
These molecules form a number of different gases that can be detected by your nose. Among these are methyl mercaptan and hydrogen sulfide, which smell like cabbage and rotten eggs respectively.
Other gases may be given off as well. Collectively, they are known as volatile sulfur compounds (VSCs). The word "volatile" indicates that these substances evaporate easily, not that they will catch fire - although a paper in the British Medical Journal from 1886 describes a case in which a man with severe halitosis lit a match in front of his face and set his breath alight.
However, his doctor suggested that the man's gut had created methane, which is not a VSC. Sulfur compounds are present in extremely low amounts in bad breath, but they are powerful enough to cause a major reek.
To alleviate them, individuals with halitosis may consider using a specialty breath freshener.