I see some US beers advertising that they brew according to the "German Beer Purity Law." What is that, and is it still relevant today?
The German Beer Purity Law, also know as the Reinheitsgebot, dictates what ingredients may be used to create beer in Germany: barley, hops, and water. It dates back to 1487, which is why you may notice the omission of yeast: it hadn't been recognized as an ingredient yet. The law was removed from the books in 1993, and replaced by another similar law which allowed yeast, sugar, and some of the more common brewing ingredients.
In the case of a US brewery making such a claim, it's a sort of advertisement toward the "purity" of their product, i.e., they don't use adjuncts (rice, etc) or other flavorings (fruit, spices) in their beer.
In addition to what's been said, the original purpose of the order was to protect consumers from brewers who used problematic (toxic/psychoactive) herbs to preserve their beer, instead forcing them to use hops. Also only using barley allowed wheat and rye to be used exclusively by bakers to keep the cost of bread down.
One could argue the tradition has kept German brewers from innovating, and also keeps a lot of interesting styles out of reach. Most Belgian-style beers, despite having a similar heritage to German styles, will include candi sugar and spices like anise and coriander. Technically, sour beers are also out. Also, a lot of the Trappist ales will use sugar adjuncts. Today, it's mostly a statement of adherence to tradition, which can carry good marketing weight. But this is beer, not marketing.
The purity law has been introduced to regulate the production of beer in the Holy Roman Empire. The original text stipulated that the only ingredients that could be used in the production of beer were water, barley and hops.
The "Reinheitsgebot" has actually survived the Holy Roman Empire. Many German brewers are proud of this heritage and claim to stick to it. It's relevance today is commercial. It's used as a label for marketing reasons.