Hikite is most commonly to describe the pulling back of a punch or the position at the side of the chest. Hikite itself indeed refers to pulling back, but not necessarily a punch. In fact, any movement after attacking with your arm can be classified as Hikite. Since we are practicing Budo, which you can see as a specialisation, words such as Hikite are not always clear.
In the summer of 2015 for example, I was in Japan. Since I can read several Kanji I was able to discover the true meaning of Nagasu on the toilet..
Of course I am not serious with this example, but it does show that the meaning of or behind a word can be quite different in daily life as opposed to using it professionally. The same goes for Hikite.
Hikite does not only describe the pulling of the hand and the end position, but also the function. In this video I demonstrate two ways of doing Hikite for Uraken and will explain which one I prefer over the other based on three reasons.