Learn Icelandic: Hann er góður dansari.

It comes from the verb dansa (to dance). By removing the infinitive ending -a and adding the suffix -ari, you create a noun for the person doing the action.

Why is the adjective góður used here instead of góð or gott?

Because dansari is a masculine noun. Nouns created with the -ari suffix for professions or doers of an action are almost always masculine, so any adjectives describing them must take the masculine form. Here, góður is in the masculine singular nominative form.

How does the suffix -ari change in the plural if I want to talk about multiple dancers?

Masculine nouns ending in -ari form their plural by changing the ending to -arar. So to say They are good dancers, you would change both the adjective and the noun: Þeir eru góðir dansarar.

How do I add the definite article to say the dancer?

Because dansari already ends in the vowel -i, you simply add -nn to the end of the word to make it definite, giving you dansarinn (the dancer).