Harry Bloomfield, Esq. wrote:
They probably listen to the noise from flowing water, the flow will not
normally be continuous, unless there is a continuous leakage. Another
way would be to listen to the tick of a water meter, which should stop
completely for long periods of no water use.

From the horse's mouth:

: How does LeakBot work?
:
: Its not magic, its science. LeakBots patented Thermi-Q technology
: accurately measures both the air and water temperatures in your home. If you
: have a leak it will continually draw colder water from outside into your
: home, creating a consistent drop in temperature. LeakBot can sense the
: prolonged and consistent drop in temperature and alerts you to the problem.

Theo