Baking is a way of cooking food with dry heat, usually inside an oven. Baking is very similar to roasting, but generally bread and cakes are baked and meat and vegetables are roasted.
Basting is a way of keeping meat moist while it is being cooked slowly, such as when it is being baked. You baste something when you pour a little liquid over it while it is cooking. Meat is usually basted with its own juices from the bottom of the pan, or with marinade.
Batter is a mixture of ingredients like eggs, flour, milk and sugar mixed together into a thick liquid. Batter is how you would describe cake, cookies, and breakfast foods like muffins and crepes before they are cooked. Batter can be used to as a coating on things like fried chicken.
Brew means to steep, stew or ferment something, usually a drink. Beer is brewed using fermented yeast and malt.
Something is browned if it develops a brownish tint as it is baked. Browning is the very first stages of something being burnt, and usually means that the food is just cooked enough.