This page gives a high level overview of the core technology underpinning Connext, particularly how it minimizes the need for the user to trust routers in the network.
At the core of Connext is a protocol for state channels.
State channels are a technology that let two parties batch up a set of transactions with arbitrary conditionality among themselves. As an example:
We can generalize this core concept in one of two ways. First, the above interaction can be extended to any type of transfer by implementing additional conditionality on how the funds are unlocked. For instance, in order to create a time-delayed payment, you could extend the escrow to unlock with both your signature and if a certain number of blocks have passed.
Second, the output of the above interaction can also be any arbitrary
There's a lot more information available publicly on state channels, here are some great resources: