There are several ways to mix ingredients to form a batter or dough. Each technique contributes differently to the final texture of the baked product. Unfortunately, many recipes use mixing terms interchangeably, which may be why your brownie did not look like the super moist one in that cookbook photo!
Cream - to beat an ingredient or mixture of ingredients until soft and smooth. Many recipes often require creaming of fat and sugar; this means to aerate and soften room-temperature fat (usually butter) by beating and blending it with sugar until it is smooth, light and somewhat fluffy. The sugar crystals cut through the fat globules in the butter, introducing tiny air pocket seeds that will expand further from the leavening gases produced during baking. This technique is usually used for cookies and cakes to create a light and moist texture.
Beat - to mix vigorously until one ingredient, or a mixture of ingredients, become smooth and thoroughly combined. Beating is a method of mixing that incorporates air into the ingredients and usually requires an electric mixer, a whisk or a fork. Beating may also refer to vigorous manual stirring using a wooden spoon or a spatula.
Stir/Blend - stirring or blending refers to a moderately gentle (but not too gentle) circular motion intended to combine ingredients evenly and create a homogeneous mixture. This can be done using a wooden spoon or rubber spatula, but not an electric device.
Fold - to gently incorporate one ingredient (or mixture of ingredients) into another without stirring or beating. Folding usually involves the addition of one light, aerated mixture (whipped cream or beaten egg whites) to a more dense/moist base mixture (batter). A rubber spatula is often used to cut down through the two mixtures, sliding the spatula across the bottom of the bowl, and then turning the mixtures over one another by bringing the base mixture up from beneath the aerated one. This technique is repeated to gently combine the ingredients. It is done to retain air within the batter and create a very light product, such as angel food cake, sponge cake, soufflé or mousse.