As the etymology of the words disgust and distaste would suggest, such emotions are fundamentally linked to food. Disgust initially served to provoke us to reject certain foodstuffs to prevent us from swallowing potentially toxic substances.(1) However, since bacterial and viral infections can be passed on by other means, not just by ingesting food, the concept soon evolved to be considered as a means of preventing infectious diseases in general.
The emotion of disgust would therefore be provoked by food an eater could not ingest for biological reasons. However, research in psychology and social sciences has shown that, even if there is no real biological reason why an eater cannot consume a certain foodstuff, this emotion can just as easily be roused if the eater cannot consume the food for socio-cultural reasons. The principle is applicable beyond the realm of food too, to any object or situation that a person simply cannot bear.(1)

All this goes on in our brains. Neuroscience shows that, when we perceive disgusting stimuli(2,3), the emotion of disgust correlates to intense activation of the anterior part of the insular cortex, sometimes in under 300 milliseconds.(4) This same anterior insular cortex is also strongly active when we process sensations of taste and smell. If this part of your cortex is damaged, you would have difficulty feeling disgust(5) or even recognising this emotion on someone else’s face!(6)

Notes et références
(1) Rozin P et al (2008). Disgust. In Handbook of emotions, 3rd ed. (pp. 757-776). New York: Guilford Press.
(2) Calder AJ et al (2007). Eur. J. Neurosci., 25(11), 3422-3428. Available here.
(3) Wicker B et al (2003). Neuron, 40(3) :655-664. Available here.
(4) These measurements were made by implanting electrodes directly into parts of the brain, in this case the ventral part of the anterior insula. This technique gives very good temporal resolution of the activation of the neurons. Krolak‐Salmon P et al (2003). Ann. Neurol., 53(4), 446-453.
(5) Mitchell IJ et al (2005). J. Neuropsychiatry Clin. Neurosci., 17(1), 119-121. Available here.
(6) Calder AJ et al (2000). Nat. Neurosci., 3(11), 1077. and Adolphs R et al (2003). Brain Cogn., 52(1), 61-69. Available here.