One of the major ideas explored in Perfume is the notion that the many elements of repulsion and attraction which we cannot explain are based on scent. Grenouille, with his preternaturally acute sensitivity to smell, realizes that when a girl is generally regarded as exceptionally beautiful—more so than her physical appearance would adequately explain—people are really being influenced and attracted to her by her scent without realizing it. This is why the power of odor is described as "stronger than that of words, appearances, emotions, or will." We understand that we are being influenced by these other factors and can therefore attempt to make allowances for them. The odors that we breathe in come to us much more directly and imperceptibly, and, as we have to breathe, we cannot avoid them.
One of the artistic triumphs of Perfume is to describe scent so clearly, despite the fact that our vocabulary in this area is so poor (one only has to look at the tortuously pretentious diction of wine critics to realize how difficult it is to describe an aroma, or, for that matter, a taste). Suskind generally has to describe smells in terms of the other senses, particularly when the smells in question are only perceptible to Grenouille himself ("the clayey, cool odor of smooth glass," for instance).
Grenouille's dizzying ascent to olfactory omnipotence is a catalog of ways in which he uses his power over scent to his advantage (to render himself inconspicuous, to secure advantageous positions, and ultimately to manipulate people's emotions). However, since he is a genius, "advantage" does not mean quite the same to him as it does to ordinary people. Baldidni, for instance, would have used such powers to become immensely rich and successful, but Grenouille is as much the servant of scent as he is its master. Once he has achieved the peak of success in the empire of odor, the rest of the world does not matter to him.
Studies have shown that there is a direct link to smells and powerful emotions; this is a fact that is evidenced to be true by the very successful market of perfumes, body sprays, lotions and other products that all have pleasing scents and make quite a bit of money in marketing it. All of my high school guy friends wore the cologne Drakaar Noir, and years later, I was walking in a store and smelled a candle that made me feel incredibly nostalgic and happy, and I had no idea why. Eventually, I figured out that the candle was based on that cologne, and smelling it was reminding me of all of the fun times I had with my friends back in the day. For whatever reason, scent elicits powerful emotions in us, and can bring back memories of people years afterwards.
In Perfume: The Story of a Murderer, Grenoille demonstrates just how completely true the quote above is. Think of the ending, for example. What drove normal, sane human beings to tear a person apart bit by bit and consume him like savages? Scent did--nothing else. Nothing in the world would have ever convinced them to do that--kill him maybe, but cannibalism? Nope. If nothing else, Suskind dedicates an entire novel to the highly underrated sense of smell, and creates a diabolical character to demonstrate its power.
I'll take a shot at answering the second part of your question, "In what ways does Grenouille use this power to his advantage?"
It's been a while since I read Patrick Sueskind's novel, Perfume, but I recall the main character Genouille uses the power of odor at least twice. (I'm sure he uses it a lot more than twice, of course.) Pretty early in the novel he is able to create a scent that will make him smell like a normal human, which renders him virtually invisible to others. When he doesn't apply that scent, people notice and avoid him; with it applied, he passes into crowds pretty much without notice. He also uses the power of scent, of course, in the powerful perfume that he constructs (or composes, I suppose might be a better word) later in the novel from the scents of the women he kills. When he applies that second scent, people pretty much do whatever he asks of them.
Scent is, as Suskind notes in Perfume: The Story of a Murderer, one of the most powerful of the five senses. It can repel or attract, cause strong emotions, and recall vivid memories. Think about how the smell of a rose makes you want to breathe in deeper, or how the smell of fresh baking bread will make you think of your grandmother. Consider also how animals use scent to mark territory, attract a mate, or deter predators. The power of scent comes precisely from the fact that "it enters into us like breath." We can put earplugs in to drown out noise, we can close our mouths to stop tasting, but we can't stop breathing, and therefore, can't stop smelling.