Honey helps baked goods stay fresh longer because, unlike common table sugar, honey is made of two so-called "simple" sugars: glucose and fructose. Table sugar also has glucose and fructose, but they're chemically bonded together in a double sugar called "sucrose." Having two single sugars instead of one double sugar means that ounce-for-ounce honey contains more sugar molecules, which is why honey is also a little sweeter than table sugar.
But the reason honey helps keep baked goods fresh has to do with the ability of sugar to attract and hold onto water molecules. All these sugars are "hygroscopic," that is they attract and hold onto water, each sugar molecule holding several water molecules. By holding onto water, the sugar helps keep moisture from escaping from the food and so keeps it tasting fresher longer.
But when two sugars, like fructose and glucose, bond to each other, they lose some of their ability to bond to water molecules. And that means your bread or cake will lose water faster. Honey's attraction to water is also why candy made from honey tends to get stickier than candy made from sucrose, or table sugar.
Commercial bakeries use chemicals like Polysorbate to keep baked goods fresh, but with honey you can do it naturally. Incidentally, if you're worried that honey will make your cake too heavy, try beating the honey until it's frothy before adding the other ingredients.
