Various herbs and spices have been added to beer to improve its flavor throughout history. Hops were first used in continental Europe, where it was noted that they helped preserve the beer as well as provided a pleasant bitterness. Hops were introduced to England during the 14th century. Nowadays, hops are an essential ingredient in almost every sort of beer.
The hops used in brewing are actually the flower of the hop vine. The hop flowers are stripped from the vines, then dried to prevent decay. Hops are commonly available to home brewers in three forms: whole, pellet, and plug. Each form has some advantages and disadvantages, and each form can be used to make excellent beer. Here is my take on the subject:
Whole hops (you may hear them referred to as "whole leaf" or "whole flower") are simply loose dried hop flowers. High quality whole hops cannot be surpassed for flavor and aroma. They can be easily removed from the wort by straining. Their physical structure, being something like a small, soft pinecone, allows them to form a filter bed that can be used to trap hot break particles after the boil. On the other hand, they don't store as well as the other forms, so getting and keeping high quality whole hops can be a bit difficult. They also behave like a sponge and absorb sweet wort, which may result in a significant loss if you are doing concentrated, partial volume boils.
Pellet hops are made by first grinding whole hops into a powder. Heat and pressure are applied and the powder is extruded through a perforated plate. In use, pellets immediately return to the powdered state and disperse when put into the boil. Pellets, because they have less exposed surface area, stay fresh much longer than whole hops. They also take up less storage volume. These advantages have led to wide use of pellet hops by commercial breweries, both large and small. On the down side, some of the more volatile aroma oils are thought to be lost during the pelletization process. Separation from the wort can be a problem, as the tiny particles tend to pack together and clog any screen fine enough to catch them. One method to deal with this is to do like the big boys do: give the kettle a strong stir to create a whirlpool. Cover the kettle and leave it alone for 15-20 minutes. The hot break and hop particles will collect in a heap in the center. Drain the wort from the side of the kettle using either a valve or a siphon. Try to get the liquid stuff out and leave the solid stuff behind. Don't worry if some of the hop and break particles get past, its no big deal. Another technique is to use a cloth bag to contain the pellets during the boil. I've used both methods numerous times and they both work.
Plug hops are really just whole hops in a fancy package. They have been pressed into ½ ounce tablets but will quickly resume their original form in boiling wort. Use them exactly as you would whole hops.
Boil time has a great effect on the amount of bittering, flavor, and aroma that hops impart to the beer. As the boiling period increases, hop bitterness goes up while hop flavor and aroma decrease. Hops boiled in excess of 45 minutes are commonly called bittering additions. Boil times from 15 to 30 minutes provide less bitterness but more flavor, hence these are sometimes referred to as flavor hops. Aroma hops are boiled 10 minutes or less. These are just generalities, of course. Bittering hops will provide some flavor and aroma, aroma hops will provide some bittering and flavor.
The alpha acid rating measures how much bittering material the hops contain. Everything else being equal, hops with a rating of 8% will provide twice as much bitterness as an equal amount of hops with a rating of 4%. The alpha acid content of hops depends on breeding (genetics) and culture (factors such as climate, soil fertility, amount of rainfall or irrigation). The alpha acid rating of hops will vary from year to year and farm to farm. The concept of Homebrew Bittering Units, or HBUs (sometimes called AAUs), was developed to help homebrewers compensate for this variation. Simply put, HBUs equal the alpha acid content multiplied by the weight. To calculate the ounces of a certain hop needed to equal a given HBU number, you divide the HBU number by the hops alpha acid rating. For example, suppose the recipe says to add 4 HBUs of Cascades. Your Cascade hops may be rated at 6.6% alpha acid. To determine how much of the Cascades to use, 4 / 6.6 = 0.6 ounces.
Beer bitterness is measured in International Bittering Units, or IBUs. Many beer recipes note the IBU content of the finished beer. The ability to predict how many IBUs your beer will contain is a powerful tool when trying to nail a style, clone a commercial beer, or just tweak a recipe. The exact amount of bitterness extracted from the hops depends on the boil time, boil volume, specific gravity of the wort, hop alpha acid content, the amount of hops, whether the hops are loose in the boil or in a bag, and whether the hops are whole or pelletized. With all of these factors involved, you can see how predicting the IBUs in your homebrew can be fairly complicated. Fear not, other folks have developed hop utilization tables and equations that make the calculations fairly simple. Norm Pyle's Hops FAQ at http://realbeer.com/hops/FAQ.html has the most complete treatment of this subject that I have seen. Highly recommended reading.
Dry hopping is the practice of adding hops directly to the fermenter. The purpose of dry hopping is to add a strong hop aroma to the beer, though some hop flavor also results. The quantity of hops used for dry hopping 5 gallons may vary from ½ ounce up to 2 ounces. The proper way to do this is to wait until the fermentation activity has nearly ended, otherwise the escaping CO2 will carry most of the hop aromatics away. Leave the hops in the beer for a week or two before bottling. I prefer whole or plug hops for dry hopping, as the larger pieces are easier to separate from the beer. I find that placing a large nylon grain bag, sanitized by boiling for 10-15 minutes, over the racking cane works well to keep the hop bits back when racking to the bottling bucket. You can also dry hop in the keg if you bag the hops, otherwise the pickup tube may clog. Many brewers worry that adding hops to the green beer will result in an infection. Forget it, it just doesn't happen.
Heat, light, and oxygen are the enemies of hop freshness, so store your hops somewhere cold, dark, and airtight. The best container is an oxygen-barrier bag, either vacuum sealed or purged with inert gas. A glass jar with a tight lid, such as a mason jar, is good. Plastic sandwich bags are lousy. The freezer is the coldest place in your house, so that's where hops belong when you aren't using them. Great beer requires fresh hops (OK, lambic excepted).
Hop varieties can be confusing. I offer these general groupings and recommendations as a way to make some sense of it all. If the particular variety called for in a recipe is not available, one of the other hops in that group will provide a reasonable substitute. This list is far from complete but it contains a fair number of the more popular types. The style suggestions are my personal preferences, you are free to develop your own.
American "C" hops (Cascade, Columbus, Chinook, Centennial) have distinctive flavor and aroma that many describe as citrus-like. They are widely used in American-style ales. Some commercial examples which feature the "C" hops are Sierra Nevada Pale Ale, Red Seal Pale Ale, Anchor Liberty Ale, and Bigfoot Barleywine. I highly recommend these hops for American pale ales, American amber ales, and American IPAs. They are not, in my opinion, appropriate in English ales, Belgian ales, German ales, or any lager beer.
English Ale hops (Kent Goldings, Fuggles, Challenger, Target, Styrian Goldings, Willamete) are not necessarily grown in England but they provide the hop flavor and aroma associated with English ales. Recommended for English pale ale, bitters, porters, stouts, English IPAs, and brown ales. Also recommended for Belgian ales.
Lager hops (Tettnanger, Hallertauer, Saaz, Spalt, Liberty, Mt. Hood, Crystal, Tradition) are recommended for lager beer, of course, but also in German ales. Many American ale recipes use a bit of these in addition to the "C" hops for added flavor and aroma complexity. Also recommended for Belgian ales.
General purpose bittering hops (Nugget, Cluster, Magnum, Perle, Galena, Northern Brewer) are commonly thought to have poor aroma and flavor, so are normally used only in early kettle additions. As an exception to this rule, Anchor Brewing uses only U.S. Northern Brewer hops for bittering, flavor, and aroma in their famous Anchor Steam. The rough and earthy flavor of Northern Brewer adds a distinctive character to this beer.