One major purpose of asana is to train the mind into one pointed focus and to bring about awareness*! When one does a pose, there usually is a physical limit. But, there is also a mental limit, which is much before the physical limit. Say, ones body can handle Navasana for 12 breaths, the persons mind might start telling them to get down from the pose by the 6th or the 7th breath. Only by bringing ones awareness totally to the present moment and to ones body, can one hold it till the 12th breath. That is done by bringing the awareness first to the mind which is racing. This calms the mind down. This teaches us to observe the mind and that is meditation.
In addition, many times, the mind constantly keeps wandering to a million places during the practice despite our best efforts. Asana helps here too. During, an asana, like say Triang Mukha Eka Pada Paschimottanasana, the calf muscles are toned and get stretched. This feeling in the calf muscle, provided its not painful, assists in naturally bringing the attention of the mind to the moment and the body and also assists in bringing back awareness to the practice and thereby assisting in meditation.
In my little experience, these are the two primary links between asana practice and meditation!
Of course, awareness of the body can be cultivated by placing the body in any awkward position. That would be stupid as we might hurt ourselves. Thats why, in the ancient research laboratories of India (read the forest ashrams of yogis :D), the yogis identified the poses in which the body can be placed in order to cultivate awareness and at the same time improve bodily health. Result is dual adavntage - health and improved awareness!
* Caveat: Awareness and attention cannot be brought about by any technique, be it yoga or vipassana. Getting rid of lack of awareness cannot be done like how one pops a pill to get rid of headache. Techniques help. But, its the individuals intention, on a 24/7 basis, that does the job primarily.