Skype was founded in 2003 by Niklas Zennström and Janus Friis. The two founders had previously created Kazaa, the peer-to-peer (p2p) music sharing protocol1. Skype was built on the idea that the cost of voice calls could be reduced by using a similar p2p protocol.
Skype even references its p2p origins – the initial name for the project was 'Sky peer-to-peer,' which eventually was abbreviated to Skype.
You can read an early analysis of how Skype p2p worked (An Analysis of the Skype Peer-to-Peer Internet Telephony Protocol (2004)). Maybe the most interesting part of Skype's architecture was how it resolved network address translation (NAT) problems. Two callers behind different firewalls (e.g., on different company internal networks) may not be able to reach each other over the internet directly. Instead, these two callers would connect through a node on the internet that had sufficient bandwidth and processing power outside of both firewalls. See a deeper technical dive (part 1 and part 2).
As Skype grew, the network started to buckle under the pressure. An hours-long outage in 2010 was related to supernodes running a bad version, then becoming overloading and failing, eventually leading to the entire network ceasing to operate (see a postmortem).
Microsoft acquired Skype in 2011 for $8.5 billion. Shortly afterward, Microsoft changed the architecture of supernodes – first only allowing its own servers to act as supernodes and then finally deprecating the entire Skype protocol.
Yet, P2p didn't mean censorship or tracking resistant. Skype censored and restricted its services in China to access that market. And in the U.S., it shared data with the NSA, allowing access to people's video and phone calls. This was all before the acquisition by Microsoft.
1 As a 10-year old I was an avid Kazaa user after Napster shut down in 2001. I probably downloaded megabytes worth of adware.