In each Expeditionary Corps building you can specify coordinated of the Kingdom that you want to explore.
After clicking the "Start" button in the building, Explorers from the building will begin to explore the specified Kingdom square by square.

If you stop Automatic Exploration of a Kingdom and then launch exploration again - the Explorers will continue the Kingdom Exploration from the square where it stopped, regardless of City and Expeditionary Corps that Exploeres are sent from. During the break in Automatic Exploration you can manually launch explorations. However, the Automatic Exploration will begin from the square where it stopped regarless of manually launched explorations and remoteness of exploration.

In case an Explorer dies in the course of Automatic Exploration, the square where he died will be explored at the end and only after that the Automatic Exploration will be completed.
In case someone's City disappears from the Kingdom Map in the course of Automatic Exploration, the empty square will be explored at the end, and only after that the Automatic Exploration will be completed.

Several Explorers from different Expeditionary Corpses that automatically explore same Kingdom - will not cross and duplicate each other in explorations.