Officially, the short title of the law was "Copyright Act 1709 8 Anne c.19", while the long title was a bit more descriptive: "An Act for the Encouragement of Learning, by vesting the Copies of Printed Books in the Authors or purchasers of such Copies, during the Times therein mentioned". It was the first law of its kind, and is now seen as the origin of copyright.
It is very interesting to look at what, exactly, the goals of the Statue of Anne were. To understand those goals, we first need to dive into history even further, before the statue came into force in 1710.
Before the printing press was invented, copying books or works was an incredibly arduous and difficult task. They had to be copied by hand, a long process which was very prone to errors. The printing press enabled the fast production of copies, and as you can imagine, authorities (both the state and the church) recognised not only its potential, but also its danger.
Some may not realise it, but the invention of the printing press is one of the most defining moments in human history. It allowed ideas to be spread faster, cheaper, and wider than ever before, and authorities quickly realised they needed to regulate access to the new technology, or else "objectionable" ideas could spread quickly, posing a threat to the state and church.
So, authorities across Europe took control of the printers, requiring them to be licensed in order to print and sell books and other works. These licenses often meant that specific works were given exclusively to specific printers. In other words, only one specific printer was allowed to print "The Unicorn and the Dead Rose", and he was allowed to prevent other printers from printing that work. In England, works also had to be added to the register at the Stationers' Company, an organisation of printers across the country. This organisation was more or less given the monopoly on printing by the state in 1662.
As you can see, the goal was to exert control over which works were printed. The Statute of Anne encompassed that idea, but added something unique, something which is by far no longer a primary goal of modern copyright law: public access to books and works. "The Encouragement of Learning" isn't part of the law's title for nothing; under the Statute of Anne, books and works did not only have to be entered into the Stationer's Company's registry, but copies also had to be deposited at the King's Library, and the libraries of Oxford and Cambridge.
Thus, as old as the Statute of Anne may be, it was incredibly ingenious. Since books and works were registered, you could always find out quite easily to whom the copyright of a work belonged. In addition, and probably more importantly, the Statute recognised the vital importance of spreading knowledge by ensuring the public could access all books and works. In modern times, copyright has nothing to do with either of those two noble goals - copyright today is about profit, and profit alone.
The terms of the Statute of Anne were relatively reasonable. Works were protected for a term of 14 years, and terms could be extended for another 14 years if the owners of the copyright were still alive and wished to do so. Books already in print were covered by a 21 year term. Today, copyright usually covers the life of the author plus either 50 or 70 years.
Even though the Statute of Anne technically protected the rights of authors, basically every author "sold" their works to publishers. When the first 21 year terms started to run out in 1731, book sellers tried to extend copyright, and argued in favour of common law copyright, i.e., copyright was a natural right of creators; it was perpetual. This is the exact opposite of the Statute of Anne, whose goal was to regulate the book trade and promote learning.
This difference of opinion led to several high-profile court cases, but the House of Lords was almost unanimous in its rejection of common law copyright. It is incredible to see that the arguments against a perpetual copyright then, in the 18th century, are the same arguments proponents of massive copyright reform use today. From a 1735 pamphlet against perpetual copyright:
Written in 1735, but still the truth today - only you should replace "booksellers" with "record labels" and "movie companies". I'm even more impressed by the words of Lord Camden (fetching fellow, or what?), who said that "knowledge and science are not things to be bound in such cobweb chains". Just... Wow.
This struggle between the idea that copyright is either natural or legislation-driven is still very much relevant today. Even though copyright is indeed a legislation-driven right, a state-granted temporary monopoly, many people view it as a natural right. While something can be said for the latter, society and mankind benefit more greatly from copyright eventually being lost.
Sadly, modern copyright is no longer about promoting learning; it is now all about ensuring endless profit for content providers. People like Lord Camden or the author of that pamphlet would be horrified by the world we live in today; a world bogged down by copyright, causing valuable works to be lost to erosion because nobody knows who the rightsholders are.
I'm not sure if you want to break out the cake and party poppers, but there you have it - copyright turned 300 today. Whoopie.