Mindfulness is a state of mind of being aware of what is, just as it is and returning to that moment instead of being carried away by our thoughts.
Thoughts WILL come by, like traffic on a busy street. They seem to demand our attention, but we don't need to do anything more than to note them and let them go by.
If our intention is to stay mindful of the present moment, we need only be aware of the passing thoughts and proceed across the street without being taken away.
This guy crossing a boulevard in Vietnam gives a graphic lesson in this metaphor for mindfulness: