Here's a specific example:
Blockchain-powered systems are an alternative to the censor-prone nature of the current networks (Internet, but also financial networks).
Governments and large corporations hold significant leverage over the omnipresent communication mechanisms that are available today. This wasn't an issue when the Internet was invented.
If a government disagrees with the existence of Wikileaks, Wikileaks can be excommunicated or financially strangled to death by applying pressure to third parties (banks or internet service providers) that allow it to function.
Blockchains and P2P networks provide an alternative to this.