This isn't the most beautiful topic, but I bet this question has been subconsciously there in everyone’s mind.
Spraying heaps of perfume, lighting up incense and using disinfectant after going to the toilet are the many ways we mask the bad feces smell. Everyone knows what bad bowel smell + lots of floral perfume smells like (smells eeewww!! LOL)
Theory has it lighting up a matchstick neutralize odors. Scientist states smell is subjective, meaning it's possible the "match effect" is in our heads. However, if you're willing to play along and assume a match really does work, there are a few possible reasons why.
When a match is struck, it produces sulfur dioxide, a "very pungent substance, to which the smell receptors are extremely sensitive." MadSci explains, "You can smell a minute amount of sulfur dioxide, but when you have done so, you will not smell anything else for a while." So, the match doesn't really get rid of the odor -- it just covers it up, or turn off your sense of smell for a few minutes. A few more theory - "oxidation of smelly substances in the flame" and "absorption of smelly substances onto the smoke."
The TV show "MythBusters" covered this topic and concluded that matches mask the methyl mercaptan found in flatulence and feces. So, a match may not eliminate odors, but it will push them to the background. Most of the time, that's good enough.
For all travelers who are sharing a bathroom/toilet, bring some matchstick on your next trip, light a few match stick after doing your business or after some heavy vomiting, while the flame is still burning slowly move the fire in circular motion around the toilet seat, repeat this step a few times, then flush. If the odor is still strong light up more matches, then flush, no-one would notice what business you were up to before they stepped into the toilet. (Just don't bring matches onto planes! buy them at your destination/s!).
If you find flushing burnt wood into our drainage system is not eco-friendly, bring a bowl of water with you before/after entering the toilet, lighting up matches without dipping it into water just doesn't get rid of the smell correctly.
Even at home, keep match boxes in the toilet, its much better then using perfume spray, which just mask the smell. I really don’t know how it works but personally, the burning wood in water and smoke does something in the air which distinguish the feces smell