The greatest benefit of the internet is the ability to reach information from all around the world that would otherwise be inaccessible and to use that information to communicate and collaborate with others. The web turns many individuals into an interconnected entity, capable of much more than the sum of the part, much like a colony of ants or a flock of birds. One of the best known examples of this is Wikipedia, which uses minor imputs from many sources to build an encyclopedia. Pretty much all open-source software isn't written by one author or any particular group of engineers, but is based on inputs from uncountably many people. For instance, right now I'm writing this post using Firefox, the code of which can be obtained, read, and edited by anyone.
As computers chips are becoming more cheap, the great advances in processing power come not from making denser chips, but from linking together several chips to form a mini-network within a single computer. A Pentium quad is 4 chips that are networked together and distribute processing duties between each other. This makes the computer smarter. And the internet allows us to do the same with human brains.
The neatest example that I've come across is described this article.
The story is as follows: Timothy Gowers, a mathematician who won the Fields Metal in 1988, wanted to find a simple proof to something known as the HalesJewett theorem (the details of the theorem aren't too important). Normally, when one seeks a proof, he locks himself in a room with a chalkboard for long periods of time. He may consult his peers at his university, he may read books, he may look through papers, but the majority of thinking takes place within one brain. It's serial. Gowers had a better idea. Instead of retreating to a dark room, he posted a section on his blog asking for help with the proof. Anyone from around the world could contribute to the idea by posting a comment. He hoped, in this fashion, to link together the brains of people from all around the world. Gowers eventually received hundreds of comments and, over the course of a few weeks, using the ideas in these comments, he was able to piece together a simple proof.
This demonstration is both fantastic and somewhat obvious. People's brains work in many different ways, and no two people think alike. When working on a problem, it can become very easy to get stuck in a singular mindset. But by combing brains from all around the world, great things can be achieved, even if each person only contributes one small part of an idea, or only nudges the project slightly in a particular direction.
Parallel human brain processing. Pretty fascinating. Though, I'm afraid to ask how many inane "comments" the poor mathematician had to wade through between each substantive remark.