Deep neural networks are a type of machine learning that are automatically trained to see patterns in large datasets.
One example you may have used is a Google image search which allows you to search for “pictures of labrador puppies” and get the correct results even though humans didn’t manually choose each of those pictures. Instead an automatically trained deep neural network is able to give you the correct results.
In the case of SmartRhythm, the deep neural network is trained to identify heart rate/activity patterns. You can read more about SmartRhthym deep neural networks here.