If we are caught up in a feeling or distracted by thoughts in this moment, we are not fully aware of or present in this moment—mindlessness. We are also being mindless if we are aware of this moment, but unwilling to be present in it—for some reason this moment seems undesirable or unacceptable. Examples of mindlessness are:
Reading a few sentences and being unable to remember what was just read
Rushing to get something done without attention to the process of doing it
Eating without noticing textures and flavors
Unaware that we are ruminating about the past or worrying about the future
Inability or unwillingness to notice and accept uncomfortable emotions or sensations.
We are rarely mindful throughout the day. With ease we are lost in our daily routines, mindlessly accomplishing various tasks and responsibilities. We often lack the presence to fully appreciate the fruits of our labor—what we work towards for our enjoyment.
We might choose mindlessness instead of presence in mundane tasks that we wish we could avoid (e.g., paperwork, cleaning, commuting). However, when we are mindless in our pleasures (e.g., eating, entertainment, and free time) it is a tragedy, because we work hard to have them. Furthermore, the times when we are present and aware, we frequently resist this moment—it somehow isn’t quite good enough or there is something uncomfortable about it. In this resistance we deny ourselves the ability to accept and appreciate what this moment can offer.
Teacher Thich Nhat Hanh often references the two ways to wash the dishes.
The first is to wash the dishes to have clean dishes. The second is to wash the dishes to wash the dishes. 
In the second option, perhaps you feel the textures of the dishes, water on your skin, steam in the air, or smell of the soap. This is not intentionally to make the task more pleasant, although moments in which we are fully present are often more pleasant, it is just another moment with it's own qualities. And bonus: the dishes will be clean in the next moment.
1. Thich Nhat Hanh. (1975). The Miracle of Mindfulness.