Beer is essentially just four things: malt, hops, yeast and water. The process of making beer is called brewing which takes place with the fermentation of sugar from starch based material.
The most common material used is malted barley, but can also be wheat, corn, rice or any other number of things. The first step in the brewing process is called malting the barley. Barley is common because it is more suitable for brewing then baking. The mixture of malts that is used in the recipe is called grist. During this process the starch source (usually malted barley) is seeped in water, where malt enzymes break down the starch molecules which produce a sugary liquid called wort.
This is when the hops are added in. Hops are a type of flower that is best suited for beer because it is a natural preservative as well as providing bitterness, flavor and aroma to the beer. If a beer recipe calls for herbs or fruits to be added, then those are added after the hops.
Yeast is then added to cause fermentation which produces alcohol and other waste products from the anaerobic respiration of the yeast. There are two main types of yeast: ale yeast and lager yeast. The ale yeast cools at about 60 degrees Fahrenheit while the lager yeast cools at about 50 degrees. The ale yeast contributes a lot of flavor to the overall beer.
While craft beer has become bigger and bigger, many still have no idea what the term means and use it quite loosely. The Brewer's Association defines Craft beer as "those who qualify for the Tax and Trade Bureau's small brewers excise tax differential by producing less than 2 million barrels annually". While there have been arguements against this definition and may need to be tweeked in the future, I feel that it is the most complete definition and should be known and used by all craft beer fans.