We all have heard about the famous ''continuing the yoga out of the mat'' quote. Maybe it's easier to tackle the question case by case... A good way to start this is to recognize the attitude helping us to achieve our goals on the mat and keep it out as well. For example, for most of the people the problem to come to the Crow Pose is that they are not really conscient about the alignment mistakes they do such as the position of the wrist, fingers,elbows, the inclination of the arms and legs, the focus on when and which muscle to squeeze and where to switch the intensity. This Asana is not the most strength/flexibility demanding Asana, but it requires a lot of focus and self awareness; the yogi should be able to feel each part of his/her body at that moment and control it. Ans this is one of the major reasons one should focus on if he/she chose yoga instead of some other activities.
Soon, this awareness becomes a habit, and one improves also the posture, knows how to handle the body in particular situations etc... And this is why they say ''Yoga brings light to every corner of the body''. And this could be one thing to start out of the mat: Facing the dark corners of our own personalities. Having the will & strength of facing the untamed parts of ourselves, the parts which needs to be trained and refined; so in a reaction of anger, jealousy, bitterness,etc... instead of shifting the responsibility to others, choosing to face it and as we do when learning to come to the crow pose, understand our weakness and focus on the alignment, on each part of the situation, on each movement & action until we come to our aim & it's perfection.
This is just a simple illustration of how the practice of yoga gives the taste of moving energies on the mental level as well. Once the yogi starts achieving his/her Asana goals, soon understands the trick to change his/her life as well.
Wish you a week full of awareness,