There are two types of intention within Taiji Form: yang intention and yin intention.
Yang intention is active and leads to physical action. Yin intention, by comparison, is more passive and rides on the movement created by the yang intention. This can be observed when pushing a swing: the initial push is yang, then the yin intention rides the path of the swing as it returns towards you in order to push again.
Drawing a bow: yang is the draw and aim, yin is realesing the arrow.
Pushing a car to get is started: the initial effort to get it moving - yang, once it's moving less effort is required - yin.
We all have little jobs at home we intend to 'get around to' one day. This is a yin intention and will only become action once it shifts to a yang intention.
The Taiji Classics say 'the Mind leads the Qi, the Qi leads the body'. All action begins with a thought. If the thought remains just an idea in your head, it doesn't connect with the Qi so the body isn't moved. When the intention is strong/clear enough the process follows through into action.
One aspect of Taiji practise is to develop this process within each posture. When this becomes second nature the same process will be there in your everyday actions and decision making.