It can be said to be a fixing of your awareness to the sensory inputs from your six-sense media faculties from moment-to-moment.
It can also be said to be the "freeing" of your awareness--or the opening of your awareness--to the six-sense media from moment-to-moment, rather than allowing the mind to become entangled with objects and carried away with them.
It used to confuse me a lot too, because I was always so deep inside my own head that mindfulness was a really foreign concept until I thought about how I consumed the world via sensory-experience as a child, long before the mind was so heavily bogged down with memory and a habit of projecting into the future.
One thing that can be helpful is to pick one of the senses and pay keen attention to its momentary experiences. This is how I "warm up" for a session, often. I use sound, because it's easier for me, and I pay attention to my hearing as each moment arises and passes, even if I'm hearing nothing at all. Once the mind has settled some, then I slowly begin opening up that moment-to-moment awareness to my other senses.
tldr; /EL15 version: Mindfulness is paying attention to the experience of "self" through each and every moment of time as it passes