The insular cortex is situated in the lateral sulcus that separates the parietal and temporal lobes. 

It is considered to be part of the limbic system and thus is involved in emotion. 

More specifically, the insular cortex is involved in representing the body and subjective emotional experience.  According to Antonio Damasio, the insular cortex helps in the mapping of visceral states that are associated with conscious feelings and with consciousness more generally.   For Damasio, emotions are central to homeostasis and the regulation of life processes. 

Since homeostasis is about protecting the organism from harmful environmental changes, we can think of the insular cortex as helping to “insulate” the organism from dangerous conditions.

The insular cortex is also implicated in addiction.  Some research suggests that cigarette smokers who suffer damage to the insular cortex experience a dramatic decrease (and in some cases complete suspension) of their addiction.  So, when working properly it seems to play a role in maintaining addictions, and hence one might find the insular cortex somewhat insulting.