Obelisk is a distributed consensus algorithm that aims to improve on the security of other consensus systems like proof-of-work and proof-of-stake. It was created by the developers of Skycoin.
Obelisk has been described as a "web of trust", meaning that influence is distributed over the entire network as nodes are strung together in an interlocking web. Trust can be obtained by having nodes subscribe to each other. Nodes with the highest degree of subscribers are considered most trustworthy and therefore have the most influence over the network. Every node is assigned a blockchain to ensure complete transparency, where every action the node makes is publicly recorded and visible. In addition to this, every node is addressed only by its unique public key so that each has a unique identity. These processes create a system of checks and balances where the community and other nodes can audit the behavior of the network with a high degree of accuracy.
The idea for Obelisk first came about in June of 2014 and was discussed publicly in a Bitcointalk thread.