Mindfulness in everyday life means being fully attentive, alive and awake in every way. When one washes the dishes, they are only doing the dishes and are completely involved in that task. There is no need to be in the future or past or to be multitasking or daydreaming. This person can engage and be content with the current moment.
As far as recognizing the moment, I think the experience is similar to when artists and performers talk about “flow”. In this “state” the person is fully connected with the project, words or action. Their actions flow almost effortlessly, they are no longer only in their heads. The mind and hearts are working together, and concerns seem to vanish because there is no fear or need to focus on the next moment. It feels as if the person is finally alive.
Another example is when you hug someone you loved. Perhaps, the person has been gone for a long time. When you finally get to embrace them then suddenly all the noise stops in your head and your awareness is simply on that direct experience and sensations of that hug.
A person who is mindful in everyday life feels, sees and experiences every moment fully, completely and without fear or judgment.