Okay, so obviously Febreze can't make odor disappear. Odor isn't some intangible thing -- smells are caused by molecules that evaporate into the air and activate receptors inside our noses, signaling the presence of a particular chemical cocktail to our brains.
So since smell is made up of matter (however tiny) it can't actually be destroyed, based on the laws of the universe and all that jazz.
However, sprays like Febreze do more than just covering up smelly molecules with even more pungent ones. They use chemical compounds called cyclodextrins to literally trap odor molecules.
These compounds (which are made of sugar molecules) form a ring with an extremely hydrophobic center. Hydrophobic things tend to attract other hydrophobic things, and that means that aromatic molecules that are hydrophobic tend to end up in the center of the ring -- and once they're there, they get stuck. That means they're not floating around on the air anymore, and they're not going to activate your odor receptors.
It's like invisibility spray for bad smells.
Because smells are made up of such a complex symphony of individual molecules, even trapping just the hydrophobic aroma molecules tends to take away any identifiably bad smells.
Meanwhile, perfumes added to the Febreze mix -- presumably ones that are hydrophilic instead of hydrophobic, limiting their tendency to end up stuck in cyclodextrin rings -- further mask these now neutralized smells.
The overall effect gives Febreze its power: Instead of making a room smell like dirty socks plus a heavy dose of fake fruit, it makes a room smell like something unidentifiable (and hopefully neutral) -- plus a dose of fake fruit.