Spearmint &Alcohol
You're probably familiar with the scent of spearmint, and maybe at one time in your life you've eaten a slice of caraway seed cake. The molecules that give spearmint and caraway their odor have the same chemical formula, but they are mirror images of each other, and that slight alteration is the only reason spearmint and caraway smell so different. Dimethyl ether is a gas at room temperature; ethanol has the exact same chemical formula, but at room temperature it's a liquid. The only difference is the structure -- and as you can see, it makes a big difference.
Properties
Molecules with the same chemical formula but different structures can sometimes have markedly different properties, because their structure affects the way they interact with other molecules. Ethanol, for example, has a hydrogen atom attached to an oxygen, so it can interact with other ethanol molecules by forming hydrogen bonds. Dimethyl ether, by contrast, is unable to do the same. The hydrogen bond interaction gives ethanol a much higher boiling point. The different structure of the two molecules also ensures that they undergo different reactions. Ethanol, for example, will react with a chemical called Jones reagent to make acetic acid, whereas dimethyl ether will not.
Enzymes
Structure is especially important in biochemistry. In your body, molecules called enzymes catalyze important reactions between molecules called substrates. The part of the enzyme that interacts with the substrates is called the active site, and the shape of the active site is critical, because it determines which substrates the enzyme can use. The active site is shaped in such a way that only certain substrates can fit, just as only one kind of key can fit in the lock on your front door.
Biology
Much the same is true for many of the other proteins that play important roles in your body. Your sense of scent detects odors, for example, because molecules of vapor bind to specific proteins in your nasal cavity called olfactory receptors. Each olfactory receptor can only bind molecules that have a complementary shape, just as your right hand will only fit into a right-handed glove, and that's how your brain distinguishes between the scent of spearmint and the scent of caraway -- the two mirror-image molecules bind to olfactory receptors on different nerve endings in your nose.