Marsala is a fortified wine—a wine that contains a distilled spirit, usually brandy—originating in Sicily. Similar in general flavor profile to Madeira, the wine is often used for cooking (Chicken Marsala, anyone?), but it can also be enjoyed as a sipper.
Often, a recipe will call specifically for either sweet Marsala or dry Marsala. So what's the difference? Used in the context of a savory recipe, where a Marsala is used to create pan sauce for example, the flavor distinction between sweet and dry will be so slight that substituting one for the other is really no big deal.
Sweet and dry Marsalas are both made by the same method, but as you may imagine, sweet wine simply has a higher sugar content. Given its sweeter flavor and more viscous consistency, sweet marsala is best used in desserts, like tiramisu and zabaglione, or as an after dinner drink. Dry Marsala is better suited for drinking as an apéritif or for savory recipes.