Mindfulness in ACT is basically about cultivating a different attitude to your thoughts and emotions.
Its kind of hard to explain. But basically its about creating a little distance between you and your thoughts so that you don't get hooked or buy all your thoughts. ACT gives you strategies to due this.
Acceptance of emotions particularly distressing ones (anxiety, panic ..etc) and being willing to allow them to be there is another aspect of the mindfulness incorporated in ACT.
And the final part of mindfulness in ACT is called connection, ( which I find the most difficult part!) involves focusing on what your are doing in the present moment through all five senses and not getting lost in thoughts and going on auto pilot.
I hope this goes some way towards explaining it.