だ is a copula that connects the subject to a noun complement.
Tip
Try viewing the character だ like it is an equals sign that is boxed off to the left, signifying that it only goes one way. This can perhaps act as a sort of mnemonic for what this copula does.
Example: Yui is a Japanese person
結衣が日本人だ
Info
In this example, the word for “Japanese person”, 日本人 (nihonjin) has the copula だ. This indicates that whatever is marked as the core subject (in this case, Yui) belongs to the class of Japanese person. Yui is a Japanese person (but Japanese people are not all Yui).
