the basics are covered in the paragraph:
Essentially polyelectrolytes possess many ionizable groups on their molecular chain. These ionizable groups have the property of dissociating and attaining a net charge in a variety of solvent media.. According to Alexanderowicz and Katchalsky21 these net charge groups which are attached to networks of macromolecules are called polyions and give rise to intense electric fields of the order of 1010 V/m. Thus, the essence of electromechanical deformation of such polyelectrolyte systems is their susceptibility to interactions with externally applied fields as well as their own internal field structure. In particular if the interstitial space of a polyelectrolyte network is filled with liquid containing ions, then the electrophoretic migration of such ions inside the structure due to an imposed electric field can also cause the macromolecular network to deform accordingly. Shahinpoor18,22,25,26,28,29,31-,36 and Shahinpoor and co-workers21,23,24,27,30 have recently presented a number of plausible models for micro-electro-mechanics of ionic polymeric gels as electrically controllable artificial muscles in different dynamic environments. The reader is referred to these papers for the theoretical and experimental results on dynamics of ionexchange membranes -platinum composite artificial muscles.
As well as in the next chapter
With my excuses for copy - pasting such a large amount, but it may keep others from having to study the article.
Anyway, as far as I see it, the so-called polyions (never heard that term before, but let's stay in the terminology of the paper) have the property of dissociating when a certain solvent is applied, and in dissociating generate an electric field, which causes them (and thus the polymer) to move slightly.
When movement is enforced
...shifting of mobile charges become possible due to imposed stresses.
, which again evokes an electric field.
In reverse; if a field is applied to them from the outside, the same thing will happen - the polyions will dissociate and "move".
In the first case you measure a potential if a certain compound gets in contact with the polymer (aka it acts as a sensor), in the second case it generates a small movement when a field is applied (aka it behaves as an actuator)
Precise explanations can no doubt be found in the references.
Be aware though that these explanations are only claims, and may not be generally accepted yet.
More detailed explanations I cannot give as I am not working with that type of materials, but these have to be presented in given references.