How Corda works in 5 words
Sign, Hash, Verify, Notaries, Commit.
Richard Gendal Brown does a great write up in a little more detail here.
The graphics below from the Corda documentation also help visualize how it works,
Transaction contract Sign and Hash
Work Flow, Verify, Notaries and Commit
Of course all this will not work without a network of connected nodes that talk to each other, this is provisioned by an infrastructure layer and messages are sent between nodes using Apache ActiveMQ Artemis
Zoom in on a Node
And finally the change in perception that Shared ledger technology brings.
For more in-depth technical information check out Corda’s technical documentation here.