Generally speaking, だ functions similarly to 'is' in English. Its purpose is to convey a strong sense of determination or assertion. This grammatical structure is informal, meaning it isn't used in polite speech. In a technical sense, だ is an auxiliary verb, a category of words that pair with other words to provide meaning. The word です serves the same function as だ, but is used in formal contexts and is often one of the first grammar patterns that learners encounter in Japanese. だ will consistently follow nouns or words that act like nouns, including な-Adjectives.
だ should never be attached to the end of い-Adjectives. In these cases, it is considered more correct to attach a polite equivalent, like です.
While だ is often thought of as the 'casual form' of です, that is actually not entirely true. です is a polite speech word. The official 'formal version' of だ is である. We will learn this grammar point a bit later. である can often be seen in articles, and formal writing, while です is more common in polite speech.