The ng/nk rule deals with changing the sound of certain vowels when they are followed by "ng" or "nk". Note that it can be considered a matter of accent rather than pronunciation, as you will be perfectly understood without it. In fact, in the Westfjords, NOT following the ng/nk rule is a dialectal variation, though it is dying out.
If you want your Icelandic to sound more natural and native-like, then mastering the ng/nk rule is an important step.
The ng/nk rule is a sound shift wherein certain vowels change their pronunciation when they are followed by an "ng" or an "nk". For example, langa is not pronounced with an "a", like the spelling implies, but with an “á”, since the “a” is followed by “ng”. The following table is a comprehensive list of vowels affected by the ng/nk rule.
It is worth noting that the “n” in these words is not like the “n” in núna, niðri or now, India.“n” is usually formed in the front of the mouth, touching the tip of the tongue to the teeth or the alveolar ridge (the roof of the mouth just behind the teeth). The “n” in “ng” and “nk”, however, is pronounced at the back of the mouth, just like in the English words sing, hanging, and sinking.
The ng/nk rule has two exceptions.