Your teacher should be able to give you a good explanation of what internal skills are and how they apply to your particular style of Taiji.
Internal skills are just a different method of moving the body and a different method of training the body than what is found in so-called external martial arts. All said and done, after years of diligent practice, the road leads to the same place, (or at least it should), refined whole body power.
The task of actually developing internal skills is really dictated by the individual style of IMA that you practice. Each style of IMA, whether it be Taijiquan, Baguazhang, or Xingyiquan has its different methods for training 'internal skills'. Beyond that, each sub-style of these arts also has its specific methods for training internal methods.
The best thing to do is to ask your teacher what the specific methods relevant to Chen style are. If you train the methods that are particular to your style, rather than just general methods, your progress will be much more solid.
Best of luck!