Ordinary presence is a state when one tries to retain awareness and do not get distracted. This state implies an effort and is, therefore, different from the state of rigpa, or instant presence. Being present in daily life is a very important practice in Dzogchen teaching.
It is possible to learn being present similarly to how we learn to drive a car. While driving seems difficult in the beginning and one cannot do anything else when doing it, over time this skill gets learned and one can simultaneously talk, think and look around without being distracted. In the same way, one can walk, talk, do whatever needs to be done at home or at work and even sleep and keep being present.