Unit tests are like Google Maps for your code. When you zoom in and look at small pieces, you can only go so far. However, when you zoom out and take a look from a greater distance, you can see the full path from A to B. The idea of unit testing, as it relates to LUCID development, is that it maps out all the different ways to get from one end of your application to the other. Unit tests take the question of "how does my data get from the my user's request, through my code and back to the user again?" They answer that question just like any well written application: by breaking it down into smaller more manageable chunks.
He talks some about the purpose of the tests themselves - finding the exact point where something goes wrong, answering one question at a time. He points out that testing isn't just something that's to be done when the code is first written. The tests need to be continuously groomed and updated as things change too.
You can find the first part of the series, "L is for Logging" here.