And if you have an intention, set it now.
I'm not really one for intention during yoga. I don't know what it is. I just practice. Perhaps that is my intention: clarity of mind while practicing. Perhaps I should speak my stream of consciousness and see what's going on in there. I'll admit to talking to myself sometimes. -It's supposed to help you focus on the thought you are speaking. (I'm dipping into what is more or less mindfulness.)
To me, intentionality is the destination. It's also a decision. You have to make a choice on what your intention is. Now, I'm either not good at making decisions (which sometimes I'm not), or I have no desire to set a desired outcome. I'm more about the journey, and I don't have a set destination. That's the free spirit in me. Intention is not necessarily the ultimate end goal.
Intertwined with mindfulness, intentionality gives you "strength" behind your actions. It's not knee-jerk, reactionary. It is a keen awareness behind everything you do.
The more mindful I am, the more I enjoy little, seemingly insignificant actions -such as the mere typing of these words on a keyboard. This is more than mindfulness; the deliberation behind my actions is the intention of thoughts into a tangible format.
My mantra lately has been "a stitch in time saves nine." Nothing typically break-through, but something I need to practice more.
When I do set an intention however, the results are much more fulfilling. To me, mindfulness is the JOURNEY towards your intention.